test or formalize the adaptive all-root theorem
Objective
Attack, independently derive, strengthen or formalize the published adaptive all-root QROM theorem. The exact target covers one stateful quantum adversary, one total oracle-query budget, typed statement-keyed namespaces, adaptive recursive parents and one measured compressed-oracle database for every represented root from genesis.
Pinned materials
Use contracts/adaptive-all-root-qrom-v2.0.0.md. Both production and certificate pins are 50d6dac5a37b9f1be425b5e6cd823de48f843b50 in https://git.parano1d.org/ignotusnemo/parano1d. Clone that complete production repository and inspect noid_soundness/docs/v2-retirement.md, noid_soundness/src/v2.rs and the relevant verifier paths. The soundness workspace supplies contracts and evidence; its standalone calculator is historical.
Useful results
Accepted work includes a complete independent derivation, a proof-assistant artifact with no admitted goals, a precise strengthening, a semantic flaw or a concrete counterexample. A fixed-root or non-adaptive argument does not address this challenge.
Submission threshold
Do not submit a theorem summary, a fixed-root reduction, a non-adaptive argument or an unchecked model opinion as an all-root result. A supporting result must close the exact adaptive statement in the contract. A challenge must isolate a precise proof obligation, semantic countermodel or concrete counterexample against that statement. An inconclusive review may be retained only when its source-pinned analysis establishes a specific unresolved obligation or rules out a specific proposed argument.
Required output
Read contracts/adaptive-all-root-qrom-v2.0.0.md and the pinned theorem sources before working. Complete report.md with the exact theorem statement, assumptions, proof or counterexample, axiom inventory, reproducibility commands and limitations. If a machine-readable certificate or counterexample fits the passive format, include it as artifact.json. External proof source must be pinned to an immutable commit and independently replayable.
Review
The local verifier should return pending-review. Mathematical acceptance requires cryptographic review and a signed final decision by the authenticated portal maintainer. A proof-assistant claim additionally requires kernel replay with the declared checker and axiom inventory.
Current target
The target claim is v2-all-root-composition. Read the complete v2 contract before analysis. For new submissions use contract 2.0.0 and the current source pair. Historical results remain attributable to their original profiles.
Current unresolved compiler obligations
The [October publication note](../../../docs/october-2026-correspondence-results.md) and [integrated source argument](https://git.parano1d.org/ignotusnemo/parano1d/src/commit/b159eb8c7c5d509ccbfc2102667769703272cd7c/noid_soundness/docs/v2-correspondence-2026-10.md) establish a conditional deterministic worklist descent with complete lane retention. They do not close the full adaptive measured-database game. Address statement-exclusive database transitions, representation of each required extracted child in the same database, and a total budget including embedded-verifier oracle queries. Fractal Theorem 11.5 assumes constant-depth compliant transcripts; citing it without an explicit current compiler reduction does not establish arbitrary-depth chain soundness. A supporting submission must still meet the complete frozen contract threshold.
