Construct C05 source roots and conditional header prefixes

research/h25-c05-source-roots/DOMAIN-ARGUMENT.md

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+# Source roots and the conditional prefix lemma
+
+This is a complete implementation of two limited pure functions. It is not a complete C05 inventory, genuine preparation observer, compiler model or original V03 control family.
+
+## Fixed-source root construction
+
+`source_roots` receives exactly six `(role, filename)` keys and exact bytes. It verifies each role-specific whole-source size/SHA256, emits six path occurrences with required installation mode0444, and constructs the unchanged list-valued GCC argv for each role. The known original sources contain20 literal include sites (ten per role). Whole-source binding plus independent enumeration of all literal directives establishes this fixed-source site list; the function is not a general C/preprocessor parser. Site serialization is deterministic C/loader/service order, not preprocessing event order. Identical payloads still retain distinct role/path occurrences.
+
+The returned `mode` is supplied binding data, not evidence of actual interpreter flags. Mode292 is the required installation permission, not an observation of local snapshot permissions. `CONFIGURATION`, `SOURCE_REVIEW` and `EXECUTION` remainNone selection markers; they are not an execution guard for these intentionally callable pure functions and do not activate any original gate. Returned records are data, not capabilities or an admission certificate.
+
+## Conditional ordinary-header prefix
+
+Let the supplied finite ordered effective chain be d1,...,dn, and name be the supported ordinary relative header name. Each candidate pair is `(di/name.gch, di/name)`. Under the stated no-PCH subcase, the constructor requires each reached .gch candidate to be MISSING, and records the preceding ordinary misses until the first REGULAR ordinary header. It returns that ordered prefix and its winner.
+
+Induction on the supplied chain proves the abstract first-match statement: every completed earlier pair has been recorded missing; the first regular ordinary candidate determines the returned result. Missing observations or unsupported outcomes leave the component open. Validation of all supplied facts and all chain paths precedes selection, including unused suffix paths. A later unused *lookup record* is not required once an earlier ordinary winner is reached.
+
+Agreement with the actual compiler is conditional on independently established effective-chain semantics, authentic/stable namespace facts, compatible cache state, and inactive remapping/custom header construction. The function establishes none of those premises. It conservatively rejects present PCHs, aliases, unsupported objects and read errors; those are open subcases, not proof that every legal original C05 configuration must be rejected. Root search directories, absolute includes and other unsupported forms remain outside this partial function's local domain. These local bounds do not redefine the original C05 domain or increase its caps.
+
+The [GCC13.4 PCH manual](https://gcc.gnu.org/onlinedocs/gcc-13.4.0/gcc/Precompiled-Headers.html) describes .gch consideration before ordinary headers and eligibility conditions. This is a mechanism reference, not proof of correspondence to the pinned Ubuntu compiler. The [preprocessor-options manual](https://gcc.gnu.org/onlinedocs/gcc-13.4.0/gcc/Preprocessor-Options.html) also explains why -M/-MM reports are not the unchanged original compilation: -M changes the processing mode, while -MM omits system headers. No such diagnostic was executed here.
+
+## Why this is partial C05
+
+C05 requires independent complete project/system-header/include-search/macro/compiler/specs/linker/library witnesses. A fixed point F0=R(D,Gamma), F[n+1]=F[n] union E(F[n]) is complete only after root completeness, complete applicable edge expansion, authentic/current facts, termination with no unresolved edges, and actual projection/resource bounds are proved. The first-uncovered-input argument is conditional on those facts; an empty unresolved list cannot replace them.
+
+An absence is not a zero-byte regular file. A witness JSON hash authenticates bytes, not assertions of absence or effective search order. The pure tests explicitly retain a stale-facts counterexample: identical supplied observations can return the same certificate despite a changed latent namespace. An actual observer and its ownership/currentness proof remain missing. No fake Root, owner, syscall failure or native observation is used.
+
+The exact original helper body, SHA256aa0a315110e031e19291970c9611fe5e0f91465fa20eaec51e81186099563f78, is newly retained as inert input. The call-site audit observes no `env` or `cwd` keyword on its Popen call; that does not itself qualify the inherited caller context, module initialisation or runtime operation. Full C05 still needs the installed configured-rule edge, transitive original bytes, namespace authority evidence and selected parent limits. `OPEN-EDGES.json` preserves those obligations.
+
+All original APIs, commands, source selections, source_files meaning and caps remain unchanged. Original first-error/cleanup obligations remain due for any future acquiring observer. No new trust premise, generic accounting API, universal interpreter theorem, runtime qualification, complete cost fit, performance or selected-frontier result follows.

research/h25-c05-source-roots/OPEN-EDGES.json

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+{
+  "schema": "h25-c05-source-open-edges-v1",
+  "full_c05": false,
+  "V03_family_complete": false,
+  "edges": [
+    {
+      "id": "CONFIGURED_RULES",
+      "status": "OPEN",
+      "required": "Relevant installed GCC/cc1/assembler/linker/loader package/build configuration and source correspondence, including defaults, target hooks, specs/search and embedded scripts."
+    },
+    {
+      "id": "HELPER_CONTEXT",
+      "status": "BODY_AVAILABLE_CALLER_CONTEXT_OPEN",
+      "required": "The exact aa0a3151... helper is now supplied; its Popen call has no env/cwd keyword. Bind actual inherited context and caller/pre-launch mutations before making runtime claims."
+    },
+    {
+      "id": "NAMESPACE",
+      "status": "OPEN",
+      "required": "Genuine source-owned acquisition/capture/close observer for ordered positive/negative lookups and relevant alias/directory state, under justified original stability/ownership premises."
+    },
+    {
+      "id": "EXPANSION",
+      "status": "OPEN",
+      "required": "Actual complete macro/include/include_next/PCH/specs/script/library/loader rule adapters and original bytes reached by them. Fixed project roots are not transitive closure."
+    },
+    {
+      "id": "PARENT_LIMITS",
+      "status": "OPEN",
+      "required": "Exact selected epoch_schema_v5/group01_evidence sources and record/encoding/file bounds; complete inventory fit and complete costs remain unmeasured."
+    }
+  ],
+  "original_score": 43.5,
+  "original_activity_credit_added": 0,
+  "costs": "OPEN_NOT_ZERO"
+}

research/h25-c05-source-roots/README.md

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+# C05 pure source-root and conditional search-prefix prerequisite
+
+Implements the concrete pure enabling component returned by the completed C05 ChatGPT Pro consultation: exact six-source root/argv construction and a conditional ordinary-header no-PCH search-prefix constructor. Independent executable controls check actual source bytes, all20 literal include occurrences, exact original command syntax, invalid inputs, search-order/negative-lookup discriminators and the retained staleness boundary.
+
+The6365-byte implementation is preserved byte-for-byte at SHA256438cdc6c8b003d9a1b6a41889d6ac2f3d5bed25f77b430cf3b5f63c36c4e4612. Pro authored it and reports a separate agent review with repairs; Codex independently checked the source and ran its own controls. This is agent-assisted review, not human or proof-kernel acceptance. No prototype field, fact mapping or return value is a genuine capability or runtime admission.
+
+`DOMAIN-ARGUMENT.md` states the exact partial function domains, conditional first-match proof and unproved GCC/namespace premises. `OPEN-EDGES.json` keeps full C05/V03/observer/currentness/toolchain/parent-bound obligations open. Source-root serialization is not preprocessing event order; required0444 modes and supplied normal/optimized labels are not stat/flag observations. The selection markers remainNone, while the new pure functions are intentionally callable for isolated verification.
+
+## Reproduce
+
+```sh
+python3 -B scripts/research_package.py --package research/h25-c05-source-roots --check-only
+python3 -B scripts/research_package.py --package research/h25-c05-source-roots
+```
+
+Registered normal/-O controls execute **only the new pure component**, inspect inert original C/header bytes and parse original driver/helper AST. The archived Root/provider/producer/helper is never imported or executed; no compiler/native/original-control work or actual namespace observation occurs. All nine exact inert fixtures are inside this package for functional verification and cold availability; their original local history and complete executable closure are not asserted. SOURCE-PINS.json identifies the source packet at [PR6352](https://github.com/CrocSwap/integer-mult-bounds/pull/6352) and the additional exact original helper. The package has no unmerged external executable dependency.
+
+## Scope and lineage
+
+This accurately named enabling source unit is separate from the stopped V03 round. [PR6351](https://github.com/CrocSwap/integer-mult-bounds/pull/6351) and PR6352 publish the preceding source resolutions; PR6321/6029/5864 retain original lineage. PR6339's identity/ordinary-cleanup repair and PR6346/6347's separate custody/interpreter findings are not adopted or replayed here. Base7c49fe32c55de02c2c873655c804b16e4c3fef0a; source snapshots and original gates unchanged.
+
+## Open next questions
+
+Establish exact installed toolchain configuration/source correspondence and actual caller context, then construct complete rule adapters and a genuine stable namespace observer. Do not replace that work with a manually asserted complete inventory, raw witness hash, helper callback or category count. See TASK.json and OPEN-EDGES.json.
+
+Full original C05 and V03 remain incomplete. Original weighted43.5% (22/49), stage gates20%, overall milestones10%,24-component denominator and O03 status are unchanged. Original preparation/native execution remains unadmitted. All unmeasured physical/preparation/review/publication/final metadata costs remain OPEN_NOT_ZERO; no scientific budget, fit, gain or kappa claim.
+
+## Credit
+
+Chris R / Clear1nsight with substantial ChatGPT Pro source construction/agent review and OpenAI Codex independent source/controls/publication assistance. Retain original source/review authors, PR6321/6029/5864, unpaidmoon/Cursor Grok for PR6339 and Douglas R. Colkitt's circuit/network/native/verification lineage. Snapshots/notices unchanged; new source/controls/analysis Apache-2.0.

research/h25-c05-source-roots/SOURCE-PINS.json

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+{
+  "schema": "h25-c05-source-roots-pins-v1",
+  "pure_component": {
+    "path": "source_roots_v1.py",
+    "bytes": 6365,
+    "sha256": "438cdc6c8b003d9a1b6a41889d6ac2f3d5bed25f77b430cf3b5f63c36c4e4612"
+  },
+  "snapshots": [
+    {
+      "path": "snapshot/areas/field-variant-producer-v2/variant_driver_v1.py.txt",
+      "origin": "areas/field-variant-producer-v2/variant_driver_v1.py",
+      "bytes": 41337,
+      "sha256": "cdb1479253358508088f8aa0e1e92e6c75ffcc127e54552698598a02de061254"
+    },
+    {
+      "path": "snapshot/areas/field-variant-producer-v2/CONDITIONS.json",
+      "origin": "areas/field-variant-producer-v2/CONDITIONS.json",
+      "bytes": 6940,
+      "sha256": "70e237d6ee4ac2ccaadf01615e8106999718eb1fbb3cf7644c9fc6d3fd4463fe"
+    },
+    {
+      "path": "snapshot/stages/combined-finite-v8/integration/cold_build_evidence.py.txt",
+      "origin": "stages/combined-finite-v8/integration/cold_build_evidence.py",
+      "bytes": 16463,
+      "sha256": "aa0a315110e031e19291970c9611fe5e0f91465fa20eaec51e81186099563f78"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/pyinit_failure/dict_probe_fields_v1.c.txt",
+      "origin": "areas/field-negative-variants-v1/pyinit_failure/dict_probe_fields_v1.c",
+      "bytes": 17806,
+      "sha256": "e0188999d41a9ab26e8d3d5c37b18b2238b3af21b1db90895f01f7be76d50b65"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/pyinit_failure/field_loader_snapshot_v1.h.txt",
+      "origin": "areas/field-negative-variants-v1/pyinit_failure/field_loader_snapshot_v1.h",
+      "bytes": 19495,
+      "sha256": "bf7ab049cea89c0a882b279e35b1383ac8f99b66aa4b9b8e1ca22eb9c24c5a8d"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/pyinit_failure/field_service_v1.h.txt",
+      "origin": "areas/field-negative-variants-v1/pyinit_failure/field_service_v1.h",
+      "bytes": 17354,
+      "sha256": "7656cd37503986459c4133643372fec13d3e5ad5553881f0bf0343a9a3e11abd"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/exec_failure/dict_probe_fields_v1.c.txt",
+      "origin": "areas/field-negative-variants-v1/exec_failure/dict_probe_fields_v1.c",
+      "bytes": 17806,
+      "sha256": "e0188999d41a9ab26e8d3d5c37b18b2238b3af21b1db90895f01f7be76d50b65"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/exec_failure/field_loader_snapshot_v1.h.txt",
+      "origin": "areas/field-negative-variants-v1/exec_failure/field_loader_snapshot_v1.h",
+      "bytes": 19495,
+      "sha256": "bf7ab049cea89c0a882b279e35b1383ac8f99b66aa4b9b8e1ca22eb9c24c5a8d"
+    },
+    {
+      "path": "snapshot/areas/field-negative-variants-v1/exec_failure/field_service_v1.h.txt",
+      "origin": "areas/field-negative-variants-v1/exec_failure/field_service_v1.h",
+      "bytes": 17040,
+      "sha256": "f5066831bd812e7e88fb971ba0e7ca86dbef91fc40a1a68c17b040ce474cd880"
+    }
+  ],
+  "availability": "Nine exact inert inputs retained for functional verification and cold availability; no original Git-history ancestry or executable/import-closure qualification asserted.",
+  "predecessor_source_packet": {
+    "PR": 6352,
+    "head": "b280be8dab15359159538e639b1d8c7deafc0612"
+  },
+  "new_input": "Exact original cold_build_evidence.py was found locally at the required aa0a3151... pin after the completed Pro response. It is supplied here as inert source; it was not supplied to Pro during that turn."
+}

research/h25-c05-source-roots/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    }
+  ]
+}

research/h25-c05-source-roots/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "portable-replay",
+  "priority_revision": 8,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "original_card": {
+    "id": "portable-replay",
+    "question": "Can one reproducible environment or artifact-comparison failure be repaired?",
+    "starting_points": [
+      "research/gzip-container-reproducibility/README.md",
+      "docs/ci-verification.md"
+    ],
+    "methods": [
+      "Reproduce one portability failure and add a minimal cross-environment fix.",
+      "Audit one canonical-payload comparison for omitted proof-relevant fields."
+    ],
+    "acceptance_gate": "Preserve immutable source hashes and proof-relevant content; a different compressed byte stream alone is not a mathematical mismatch.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Resolve the current selected review, separate complex/ordinary BIT/admitted BIT/outer budgets, and compare the card against live handoffs before starting. Historical ceilings require exact source/model equivalence.",
+      "scope": "Source-binding orientation only; not a scientific replay or all-size proof. Materialize selected inputs if this checkout is sparse."
+    },
+    "first_experiment": "Reproduce one specific mismatch or audit one canonical comparison for omitted proof-relevant fields.",
+    "bottleneck_link": "Portable exact checks prevent environment failures from blocking valid contributions.",
+    "allowed_variations": [
+      "One interpreter/version mismatch or one payload field comparison."
+    ],
+    "scope_change_triggers": [
+      "Removing immutable-source pins because generated compressed bytes differ."
+    ],
+    "overlap_terms": [
+      "gzip container",
+      "reproducibility",
+      "canonical payload"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Completed bounded C05 enabling component: exact six-source/20-literal-site roots and unchanged argv construction, plus a conditional ordinary-header no-PCH first-match prefix constructor. Full C05 domain, current namespace observer and original V03 family remain open.",
+  "scope_change_reason": "User authorised consulting Pro then implementing and publishing useful prerequisites, and explicitly publishing resolved questions. This is a new accurately named partial source component, not a resumed V03 round or full C05 acceptance.",
+  "bottleneck_link": "Source-bound verifier qualification prerequisites; no change to the multiplication supplier, selected result or framework assumptions.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop on source mismatch or unresolved interpretation; no target/native/compiler/original-control execution, historical allowance transfer or silent scope change.",
+  "outcome": "partial",
+  "evidence": "source_roots_v1.py, independent pure controls, DOMAIN-ARGUMENT.md, exact inert inputs and explicit OPEN-EDGES.json.",
+  "author": "Chris R / Clear1nsight",
+  "ai_assistance": "ChatGPT Pro source consultation and substantial OpenAI Codex source-audit/verification assistance. These are agent-assisted findings, not human or proof-kernel acceptance.",
+  "open_questions": [
+    {
+      "question": "Can configured compiler/helper/search/linker rules and genuine stable namespace evidence complete the original C05 domain?",
+      "why_it_matters": "Literal project include roots and a conditional prefix certificate do not account for all transitive/implicit inputs or authenticate supplied absence assertions.",
+      "first_step": "Bind exact installed toolchain build/configuration and original caller context; implement source-owned rule adapters and an actual observer with original custody and first-error guarantees.",
+      "blocked_by": "Installed-toolchain correspondence, effective search/macro/specs/linker rules, genuine namespace/alias currentness and parent record limits remain unqualified."
+    }
+  ]
+}

research/h25-c05-source-roots/VALIDATION.json

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+{
+  "schema": "h25-c05-enabling-validation-v1",
+  "observed_utc": "2026-11-02T04:05:46.377577+00:00",
+  "python": "3.12.3",
+  "source_sha256": "438cdc6c8b003d9a1b6a41889d6ac2f3d5bed25f77b430cf3b5f63c36c4e4612",
+  "source_changed_from_Pro": false,
+  "metadata_and_pins": "PASS",
+  "registered_normal": "PASS_53_CONTROLS",
+  "registered_optimized": "PASS_53_CONTROLS",
+  "project_paths": 6,
+  "literal_sites": 20,
+  "stale_facts_counterexample": 1,
+  "original_archived_sources_executed": false,
+  "new_pure_component_executed": true,
+  "full_C05_or_V03_acceptance": false,
+  "original_activity_credit_added": 0,
+  "metadata_preparation_fix": "Required Open next questions heading added after checker refusal; implementation/fixtures/controls unchanged.",
+  "costs": "OPEN_NOT_ZERO"
+}