Phase 13: Tools & Protocols

Rebuild and Prove Equal: Differential Tests, Byte Comparison, and the Evidence Loop

Type: Build

Languages: Python, C

Prerequisites: Phase 13 · 34 (lifting to pseudocode), Phase 13 · 35 (evidence, confidence, and unknowns)

Time: ~110 minutes

The Problem

You asked rea for the function dossier of percent_change in our ledger-x86_64-O1.o fixture. Ghidra 12.1.4 returned pseudocode, and the agent wrote this C from it:

cCopyint percent_change(int before, int after) {
    if (before == 0) return 0;
    return (int)(((long)after - before) * 100 / before);
}

Four tests pass: (100, 150) gives 50, (200, 100) gives -50, (0, 5) gives 0, (50, 100) gives 100. The agent also rebuilt grade as four if statements on 90, 80, 70, and 60. Six more tests pass. The report says "verified".

That report answers none of these questions:

• What does the original return when (after - before) * 100 does not fit in 32 bits?
• What does the original return for a score of 110?
• Does the rebuild compile to the same 16 bytes as the original?
• When two compiled functions hold the same bytes, do their relocations point at the same constants?
• Which evidence record did the rebuild come from, and did the agent read the listing or the pseudocode?
• What status does the proof get on a host without a C compiler?

Every target in this lesson is a program we wrote and compiled. The scope and law rules from lesson 32 apply unchanged.

What the Evidence Says

The agent loop in code/main.py made six calls to rea 6.5.0 over stdio. The recorded run is code/fixtures/runs/agent-run.json. The server answered initialize with protocol version 2025-11-25. Three calls returned Evidence records:

The first call paid for the Ghidra import and auto-analysis. Each record carries confidence: "observed", authority: "shipped-artifact", and the SHA-256 of the object, 9a4a8082ba5e285a732552981a6935e0c5255725664f380e37c44ebfb04d803f. Ghidra loads the relocatable object with .text at 0x100000, so percent_change sits at 0x100000 and grade at 0x100010.

The pseudocode for percent_change is where the long came from:

cCopyundefined1  [16] percent_change(int param_1,int param_2,ulong param_3)
{
  long lVar1;
  undefined1 auVar3 [16];
  if (param_1 != 0) {
    lVar1 = (long)((param_2 - param_1) * 100);
    auVar3._0_8_ = lVar1 / (long)param_1 & 0xffffffff;
    auVar3._8_8_ = lVar1 % (long)param_1 & 0xffffffff;
    return auVar3;
  }
  ...
}

The decompiler saw cltd and idivl write both edx and eax and modelled a 16-byte return value with a 64-bit division. The listing in the same record says something plainer:

Copy0x100000: TEST EDI, EDI
0x100002: JZ 0x0010000d
0x100004: SUB ESI, EDI
0x100006: IMUL EAX, ESI, 0x64
0x100009: CDQ
0x10000a: IDIV EDI
0x10000c: RET
0x10000d: XOR EAX, EAX
0x10000f: RET

Every operation is 32 bits wide. IMUL EAX, ESI, 0x64 multiplies in 32 bits and keeps the low half. CDQ sign-extends eax into edx, and IDIV EDI divides the 64-bit pair by a 32-bit divisor. A rebuild that follows the listing is 100 * (after - before) / before in int.

The grade record has the same shape. The pseudocode names a table, *(uint *)(&DAT_001000b4 + (ulong)uVar2 * 4), and an unreadable default expression built from 0x66666667. The listing shows the divide by 10 as IMUL RAX, RAX, 0x66666667, SAR RCX, 0x22, SHR RAX, 0x3f, ADD ECX, EAX. Then ADD ECX, -0x6, CMP ECX, 0x4, and JA keep tens from 6 to 10. XOR EAX, EAX before the compare is the default of 0. LEA RCX, [0x1000b4] and MOV EAX, dword ptr [RCX + RAX*0x4] read a table of five 4-byte entries.

Step 4 read those 20 bytes: 01000000 02000000 03000000 04000000 04000000. The table is 1, 2, 3, 4, 4 for tens 6, 7, 8, 9, 10. That is the switch in ledger.c, with case 10 and case 9 sharing the value 4.

Both proofs in rea's own evidence pages started from the listing and from read_bytes of constants. The DX-Ball first pseudocode was FUN_00406400(void) with no stack input, and the instruction view corrected it. Read the listing first. Cite the record id, then write the C.

Write the Candidates

The folder code/fixtures/candidates/ holds eight rebuilds, one function per file. Four follow the listing or compile to the same code. Four are plausible and wrong, or wrong in a way one hand-written test finds.

Each file compiles with the fixture command, clang -target x86_64-unknown-linux-gnu -O1 -fno-asynchronous-unwind-tables -c. The compiled objects are committed beside the sources so the tests run on a host without clang.

Leg One: Execute and Compare

McKeeman's 1998 definition of differential testing needs "two or more comparable systems" fed "mechanically generated test cases", and treats a different result, a hang, or a crash as a bug candidate. He named the hard part: "The ugliest problem in testing is evaluating the result of a test." The original function is the oracle here. We do not need to know the right answer. We need the original and the rebuild to disagree nowhere on a grid that reaches every hazard.

Design the grid

input_grid() in code/main.py builds 92 cells. For percent_change it takes every pair from ten before values and seven after values:

Copybefore: 0, 1, -1, 3, -3, 7, 100, -100, 2147483647, -2147483648
after:  0, 5, -5, 105, 536870911, 2147483647, -2147483648

For grade it takes 22 scores: both sides of each band edge, negatives, 0, 110, and the two int limits. classify() tags each cell. Overflow has 32 cells, negative 17, boundary 14, plain 12, and zero guard 7. Negative truncation has 5, rounding 2, beyond the switch 2, and trap 1.

Each class exists for one reason. The zero guard cells check the TEST EDI, EDI branch. Negative cells check truncating division: C and idiv round toward zero, so -9 / 10 is 0 and -10 / 10 is -1. Rounding cells check that the multiply happens before the divide, so (105 - 100) * 100 / 100 is 5 and not 0. Overflow cells make (after - before) * 100 exceed 32 bits. The one trap cell makes the wrapped product equal INT_MIN with before equal to -1.

Yang, Chen, Eide, and Regehr built Csmith to generate programs with no undefined behaviour. An oracle disagreement on undefined behaviour is noise and never a bug report. Signed overflow is undefined in C. Our oracle is a compiled object with one fixed behaviour, so overflow cells are in scope. The lesson is to know which cells rest on the standard and which rest on the compiled bytes.

The driver and the trap

code/driver.c reads one cell per line from stdin and prints the inputs, the original result, and the rebuild result. build_harness() compiles the candidate with -Dpercent_change=cand_percent_change -Dgrade=cand_grade, so both versions link into one program under different names. On an x86-64 Linux host the original is the fixture object itself. On any other host it is ledger.c compiled natively, and the report records original_kind: fixture-source.

The driver installs a SIGFPE handler with sigsetjmp and siglongjmp. For before = -1 and after = 536870911, the difference is 536870912 and the 32-bit product wraps to -2147483648. On x86-64, idiv with that dividend and a divisor of -1 raises the divide error exception. The quotient does not fit in 32 bits (Intel SDM Volume 2, IDIV). The handler turns that into the recorded value trap.

On AArch64, sdiv has no trap and returns -2147483648 for the same operands. Our run on an arm64 Mac recorded exactly that. The oracle depends on the architecture, and the report says which one ran.

Results

prove_behaviour(PLAUSIBLE) builds the long rebuild and the threshold rebuild. The ten naive cases pass. The grid fails on 28 cells:

All 26 percent_change failures are overflow cells with |before| > 1. For before equal to 1 or -1 the 64-bit quotient truncates back to the wrapped value, so those cells agree by accident. The threshold grade fails because the original switch has no case for tens of 11 and above, and 110 / 10 is 11.

prove_behaviour(EQUAL) builds percent_change_mul_first.c and grade_switch.c. All 92 cells agree. percent_change_div_first.c fails two of the four naive cases, which is the one case a hand-written test does find.

oracle_disagreements() checks a second thing. percent_change_model() and grade_model() are Python models of the listing, with wrap32() for the 32-bit multiply and idiv32() for the architecture rule. The report compares the model with the observed original on every cell. Zero disagreements means the model and the binary agree on every cell. The model is derived evidence and the run is observed evidence. The report keeps them in separate fields.

Leg Two: Recompile and Compare

Behaviour on a grid is one leg. The second leg asks whether the rebuild, compiled with the same compiler and flags, produces the same bytes. The DX-Ball project reported "63 matching bytes" for its helper. The TH04 project reported a 2,139-byte match. Each used the compiler of its own period. rea itself cannot do this. Its compare_functions line-diffs provider text and attaches the limitation "Assembly is opaque provider text; relocation normalization is unavailable."

Read the object

ElfObject in code/main.py reads one ELF64 relocatable object with struct.unpack_from. It checks the magic, the 64-bit class, little-endian data, e_machine 62, and e_type 1. Then it walks the section headers, the string table, .symtab, and every .rela section. In the fixture, percent_change starts at .text offset 0 with size 16 and grade at 0x10 with size 46. total starts at 0x40 with size 31 and grade_label at 0x60 with size 63.

The 16 bytes of percent_change are 85 ff 74 09 29 fe 6b c6 64 99 f7 ff c3 31 c0 c3. The function has no relocations. grade has one: offset 0x26 inside the function, type R_X86_64_PC32, symbol .rodata, addend 0x10. It belongs to the 7-byte leaq at offset 0x23, whose last four bytes are the displacement field.

Mask, then compare the records

In a RELA object the addend lives in the relocation record, and the four field bytes are zero. The candidate grade_switch.o also holds zero there. A plain byte compare passes while the two relocations name different places. mask_relocations() zeroes the field on both sides anyway, so the same method holds for REL objects and for Mach-O, where the field carries the addend.

Then prove_bytes() compares the relocation records by offset, type, and target section. The original says .rodata+0x10 and the candidate says .rodata-0x4. The addend differs because the candidate object has no labels.rel table in front of its switch table. A different addend is a different offset, not a different function.

Read the constants the relocation points at

For a PC-relative field that ends its instruction, the CPU adds the next instruction address, so the target is symbol plus addend plus 4. In the original that is .rodata+0x14, and in the candidate it is .rodata+0x0. read_table() reads five 4-byte entries there. Both hold 1, 2, 3, 4, 4.

The count five comes from the listing: CMP ECX, 0x4 with JA admits indexes 0 to 4, and [RCX + RAX*0x4] reads 4 bytes per index. CLAIMS in code/main.py records that shape for grade and records zero relocations for percent_change.

This step exists because of a bug the TH08 project documented. Its older comparison "replayed the target address into the instruction's relocation field, then compared instruction bytes without checking the floating-literal data at that address. Source 0.0 could therefore appear exact against target 128.0." The fix audited 1,548 floating-literal references and corrected twelve more. grade_case10_wrong.c is our version of that bug. Its 46 code bytes equal the original, its relocation record has the same shape, and its table is 1, 2, 3, 4, 3. Only the constant check fails it.

Results

Two results deserve a second look. percent_change_split.c has different source text and identical bytes, because clang treats signed overflow as undefined and folds after * 100 - before * 100 into one multiply. grade_table.c also matches byte for byte, so the compiler reached the same table from an array index and from a switch. A byte match proves that this compiler, with these flags, produced the same code from the candidate. It does not prove the candidate is the original source text.

Size is a diagnostic and not an acceptance. rea's evidence pages record a 1,825-byte candidate with the right length and 467 differing bytes. The wide rebuild is 26 bytes because movslq, imulq, cqto, and idivq replaced the 32-bit forms. The listing had told us the width before any compile.

The Agent Loop Over rea

Sixty-five of rea's MCP tools have no CLI command, and verify_reconstruction is one of them. McpStdioClient in code/main.py is the smallest client that reaches them. It starts npx -y rea-agents@6.5.0 mcp, writes one JSON-RPC request per line to stdin, and reads one JSON object per line from stdout on a thread. It sends initialize with protocol version 2025-11-25, then notifications/initialized, then tools/call. The default deadline per call is 330 s, the same number rea allows for a Ghidra cold start.

agent_loop() makes the six calls and records each one:

jsonCopy{
  "step": 2,
  "tool": "analyze_function",
  "arguments": {"procedure": "percent_change"},
  "seconds": 6.31,
  "is_error": false,
  "evidence_id": "ev_e88b10dc0c6400e51bb6f7fdc3eaea8d2c97cc02463f0db3e6afeefc273197cd",
  "confidence": "observed",
  "authority": "shipped-artifact",
  "limitations": ["Resolved reference metadata identifies computed, indirect, external, call, jump, and data edges; unresolved targetless flows remain unknown, and function classifications distinguish thunks and externals.", "..."],
  "result_sha256": "..."
}

The complete Evidence records are stored under their ids in the same file. The pseudocode and the listing the rebuild came from are part of the fixture. table_address() finds the LEA operand in the grade listing and feeds it to read_bytes. open_binary, get_evidence_bundle, and close_binary return no Evidence record and are recorded with a null id.

run_agent(live=True) drives rea when npx is on the path and GHIDRA_INSTALL_DIR names a directory. Otherwise it replays the fixture and says so on stderr. The tests go one step further. code/tests/fake_rea_server.py is a stand-in server that answers each tools/call with the recorded record for the same tool and arguments. The client and the loop run against it on every test run, with no rea, Ghidra, or Java installed.

What rea's verifier can and cannot say

rea's verify_reconstruction takes claims that point at comparison Evidence and returns pass, fail, or unknown per claim. Its fixed limitation reads "Pass means every declared claim passed; it does not establish global implementation equivalence." A claim about a function compares provider text from compare_functions. A behavioural claim compares two recorded process captures from compare_process_captures. When a source record has incomplete call coverage, a claim about calls is unknown. Nothing inside rea compiles a rebuilt function or runs it over your input grid. The two legs in this lesson are the part rea leaves to you.

rea's obligation ledger expects a proof record with predicate_type: "rea.reconstruction-proof", operation: "verify_reconstruction_obligations", confidence: "observed", and normalized_result.passed === true. No public rea tool emits one. build_proof() in code/main.py mints it:

jsonCopy{
  "predicate_type": "rea.reconstruction-proof",
  "operation": "verify_reconstruction_obligations",
  "confidence": "observed",
  "authority": "controlled-replay",
  "normalized_result": {
    "passed": true,
    "status": "pass",
    "claims": [
      {"claim_id": "percent_change.behaviour", "kind": "behavioral", "status": "pass", "evidence_ids": ["ev_e88b10dc..."]},
      {"claim_id": "grade.behaviour", "kind": "behavioral", "status": "pass", "evidence_ids": ["ev_67b6d3f9..."]},
      {"claim_id": "percent_change.bytes", "kind": "structural-function", "status": "pass", "evidence_ids": ["ev_e88b10dc..."]},
      {"claim_id": "grade.bytes", "kind": "structural-function", "status": "pass", "evidence_ids": ["ev_67b6d3f9..."]},
      {"claim_id": "grade.referenced-constants", "kind": "structural-function", "status": "pass", "evidence_ids": ["ev_67b6d3f9..."]}
    ]
  },
  "evidence_links": ["ev_e88b10dc...", "ev_67b6d3f9..."],
  "evidence_id": "ev_..."
}

The id is ev_ plus the SHA-256 of the record without the id, over sorted-key compact JSON. aggregate() is fail-closed: fail wins, then unknown, and an empty claim list is unknown. On a host without a C compiler the two behaviour claims are unknown, so the record says unknown even when both byte claims pass. authority is controlled-replay, because the proof comes from our own harness and not from the object file alone.

What the Research Says

Liu, Raff, and Micinski measured eight decompilation systems in nine configurations in 2026. Candidates that passed every test the benchmark includes still diverged on fuzzed inputs. The rate was 4.9 percent overall and up to 13 percent for one system. On 300 GitHub library functions and 287 CVE-grounded functions, the strongest refinement model raised Ghidra's build rate from 75 percent to 90 percent. Over the same functions the behavioural match rate fell from 74 percent to 62 percent. They traced the cause to invented fields, types, callees, and guards that replaced the visible unknowns a traditional decompiler leaves behind.

Our percent_change_wide.c is one of those invented types. The pseudocode offered a long, the rebuild kept it, and the result compiled, passed ten tests, and failed 26 overflow cells. The grade-threshold rebuild is an invented guard. Both would count as re-executable under the LLM4Decompile metric, which recompiles the output and runs the benchmark's assertions. Ghidra's own pseudo-C passed 20.12 percent of those assertions on HumanEval-Decompile.

DecompileBench measured 23,400 functions from 130 real programs. It found LLM methods 52.2 percent lower on functionality correctness than industrial decompilers, with higher understandability scores.

The three proofs the field uses are the three legs you can build. Phoenix and DREAM recompile the output and run the original program's tests. McKeeman and Csmith run generated inputs against the original with inputs kept inside defined behaviour. Ramos and Engler check two C functions with bounded symbolic execution, which proves equality on all explored paths up to an input size. This lesson builds the first two. The third is the practice lab in lesson 35's evidence ledger when a grid is too small to trust.

Build It

Run the standard-library harness:

bashCopycd phases/13-tools-and-protocols/36-rebuild-and-prove-equal
python3 code/main.py

With clang on the path, the demo compiles both candidate pairs and runs 92 cells for each. It recompiles eight candidates, replays the agent run, and mints the proof record. Without clang it reads the committed objects and reports the behaviour claims as unknown.

Expected shape on an arm64 Mac:

jsonCopy{
  "host": "aarch64 Darwin",
  "originalKind": "fixture-source",
  "gridCells": 92,
  "plausible": {"naivePassed": true, "gridMismatches": 28, "oracleDisagreements": 0},
  "equal": {"naivePassed": true, "gridMismatches": 0, "oracleDisagreements": 0},
  "legTwo": {
    "percent_change_mul_first": {"status": "pass", "reasons": []},
    "percent_change_wide": {"status": "fail", "reasons": ["size 16 vs 26 bytes"]},
    "grade_case10_wrong": {"status": "fail", "reasons": ["referenced constants differ: [1, 2, 3, 4, 4] vs [1, 2, 3, 4, 3]"]}
  },
  "agentRun": {"mode": "replayed fixture", "server": {"name": "rea", "version": "6.5.0", "protocolVersion": "2025-11-25"}},
  "proof": {"status": "pass", "evidence_id": "ev_..."}
}

Read code/main.py in this order:

1. wrap32(), c_div(), idiv32(), and the two *_model() functions hold the integer semantics of the listing.
2. input_grid() and classify() build and tag the 92 cells.
3. build_harness() and execute() compile one program from the original, the renamed candidates, and driver.c, then run the cells.
4. prove_behaviour() returns the leg-one report with mismatches and model disagreements.
5. ElfObject reads headers, symbols, and .rela records. mask_relocations() and read_table() prepare the compare.
6. prove_bytes() returns the leg-two report with sizes, masked ranges, relocation shape, and tables.
7. McpStdioClient and agent_loop() drive rea and record each step.
8. build_proof() and aggregate() mint the fail-closed record.

Use It

To prove a new function equal, repeat these steps:

1. Fetch analyze_function for the function and record the evidence id. Read the listing before the pseudocode.
2. Write the candidate from the listing's operation widths. Keep the original's function name.
3. List every multiply, add, subtract, and divide in the listing. Add grid inputs that wrap each one at its width.
4. Add both sides of every compare constant in the listing. For grade those were 6 and 4 after the subtract.
5. Add every divisor that can trap on the target, and record which architecture ran the grid.
6. Run both legs and read the reasons before the status.
7. Keep the proof record beside the candidate. Its evidence_links tell a reader which records the claim rests on.

Rerun both legs after any compiler update. A byte match is a statement about one compiler with one set of flags.

Interactive Lab

Lab A: the model and the run

From the code directory, open Python:

bashCopycd phases/13-tools-and-protocols/36-rebuild-and-prove-equal/code
python3 -q

Run:

pythonCopyfrom main import *
percent_change_model(3, INT_MAX)
percent_change_model(-1, 536870911, "x86_64")
percent_change_model(-1, 536870911, "aarch64")
report = prove_behaviour(PLAUSIBLE)
report.naive_passed, len(report.mismatches), report.mismatches[0]

The first call gives -133, the wrapped product divided by 3. The second gives 'trap' and the third gives -2147483648. The report shows ten naive cases passed and 28 grid cells failed. Compare report.oracle_disagreements with an empty list.

Lab B: read the object

pythonCopyobj = ElfObject(ORIGINAL_OBJECT)
grade = obj.function("grade")
grade.size, grade.data[0x26:0x2a].hex(), grade.relocations
read_table(obj, grade.relocations[0], 5, 4)

The field bytes are 00000000. The relocation names .rodata with addend 0x10, and the table reads [1, 2, 3, 4, 4].

Lab C: break one constant

pythonCopyreport = prove_bytes("grade", CANDIDATES / "grade_case10_wrong.o")
report.masked_equal, report.relocations_match, report.tables_equal, report.reasons()

The bytes match, the records match, and the tables do not. Now edit grade_case10_wrong.c so case 10 returns 4 again, recompile it with the fixture command, and watch the status change to pass.

Lab D: drive rea

With rea 6.5.0 and Ghidra 12.1.4 installed:

bashCopyGHIDRA_INSTALL_DIR=/opt/homebrew/Cellar/ghidra/12.1.4/libexec \
JAVA_HOME=/opt/homebrew/opt/openjdk@21 \
python3 code/main.py --live

The first analyze_function takes several seconds while Ghidra imports the object. Compare the new evidence ids with the committed run. The same bytes under the same analysis profile give the same ids, because the id is a content hash that excludes the file path.

Practice Lab

Extend both legs to total and grade_label from the same object.

Requirements:

• For total, the input is an array and a count. Build cells with count 0, a negative count, one element, and sums that wrap at 32 bits.
• For grade_label, the function calls grade inline and reads labels.rel, a table of five relative string offsets with their own relocations in .rela.rodata.
• Add a CLAIMS entry for grade_label with two relocations and a table of five 4-byte entries, and compare the strings the entries point at.
• Record which cells the model and the run disagree on, if any, and explain each one from the listing.
• Add one claim per leg per function to the proof record and keep the aggregate fail-closed.

Success means the proof record lists four functions, every claim carries an evidence id, and grade_label fails when one label string differs.

Output Skill

This lesson produces outputs/skill-rebuild-and-prove-equal.md. Use it to turn function evidence and a candidate rebuild into a two-legged proof and a proof record. The skill requires the listing before the pseudocode, a grid with every hazard class, relocation masking plus a constant check, and a fail-closed aggregate.

Verify It

Run the demo and the test suite:

bashCopycd phases/13-tools-and-protocols/36-rebuild-and-prove-equal
python3 code/main.py
python3 -m unittest discover -s code/tests -v

The 35 tests prove:

• c_div() truncates toward zero and wrap32() follows two's complement
• the model gives -133 for (3, INT_MAX), trap for the trap cell on x86-64, and -2147483648 on AArch64
• the grid has 92 cells and every hazard class, and the naive cases avoid every hard class
• the ELF reader finds four functions at the recorded offsets and sizes
• percent_change is 16 bytes with no relocations and grade has one R_X86_64_PC32 at 0x26
• the relocation field bytes are zero and masking changes nothing in this RELA object
• all eight committed candidates reach the expected status, with the recorded reasons
• grade_case10_wrong passes masked bytes and fails only the constant check
• the recorded leg-one runs show ten naive passes, 28 mismatches, and zero model disagreements
• with a compiler, both pairs rebuild and rerun with the same outcome
• the agent run targets the committed object by SHA-256, in order, with ev_ ids on every Evidence step
• the read_bytes record equals the table the ELF reader finds
• the client drives the fake server and records the same evidence ids as the real run
• an error result from the server goes into the run record
• aggregate() is fail-closed and the proof id recomputes from its content

Production Failure Modes

Operational Rule

Write the rebuild from the listing and name the record it came from. Run it against the original over a grid that wraps every intermediate and crosses every compare constant. Recompile it with the original flags, mask the relocation fields, compare the records, and read the constants they point at. Record each claim with its evidence id, and let an unverified claim stay unknown.

Further Reading

• McKeeman, Differential Testing for Software, Digital Technical Journal 10(1), 1998
• Yang, Chen, Eide, Regehr, Finding and Understanding Bugs in C Compilers, PLDI 2011
• Ramos, Engler, Practical, Low-Effort Equivalence Verification of Real Code, CAV 2011
• Schwartz, Lee, Woo, Brumley, Native x86 Decompilation Using Semantics-Preserving Structural Analysis, USENIX Security 2013
• Liu, Raff, Micinski, When LLM Decompilers Recompile More and Preserve Less, arXiv 2609.05370, 2026
• Gao et al., DecompileBench, Findings of ACL 2025
• Tan et al., LLM4Decompile, arXiv 2403.05286, 2024
• System V gABI, Chapter 4, Relocation
• x86-64 psABI repository, relocation types
• Intel 64 and IA-32 Architectures Software Developer's Manual, Volume 2, IDIV
• Arm Architecture Reference Manual for A-profile, DDI 0487, SDIV
• rea 6.5.0 MCP contracts
• rea 6.5.0 reconstruction obligation ledgers

This free lesson is part of the AI Engineering from Scratch curriculum. Read the full explanation, run the lesson code, and verify the result in the interactive reader or from the repository source.

Browse the complete course catalog or open this lesson on GitHub.