{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:V4NHCTIZ7I2NKIH6A2EIKFCZGI","short_pith_number":"pith:V4NHCTIZ","canonical_record":{"source":{"id":"2605.17022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-16T14:48:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a7117ec1c018348272685a2541d3a37a65c3f9a98f7d18f0e22b53b0db9b402c","abstract_canon_sha256":"3944e428e92576fe038bad3b12febbb6000302cc5e08e9c3249bc2630da26b75"},"schema_version":"1.0"},"canonical_sha256":"af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4","source":{"kind":"arxiv","id":"2605.17022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17022","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17022v1","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17022","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"V4NHCTIZ7I2N","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_16","alias_value":"V4NHCTIZ7I2NKIH6","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_8","alias_value":"V4NHCTIZ","created_at":"2026-05-20T00:03:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:V4NHCTIZ7I2NKIH6A2EIKFCZGI","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-16T14:48:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a7117ec1c018348272685a2541d3a37a65c3f9a98f7d18f0e22b53b0db9b402c","abstract_canon_sha256":"3944e428e92576fe038bad3b12febbb6000302cc5e08e9c3249bc2630da26b75"},"schema_version":"1.0"},"canonical_sha256":"af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:36.415089Z","signature_b64":"9MIPuKhR7vS2dkifGgJ2r04mAVb0sxaVqpjE9nh/arUUgaIxOuV2Nivv/pYcTgNmFB3Re3d0oXdTXMqgcS8PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4","last_reissued_at":"2026-05-20T00:03:36.414087Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:36.414087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17022","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SHBmM2l77lINccidQwNLReb1h/cTKDEuKevvbZizhf0Q/vMxd6Jz4G3ycY1JjxGbmSNDxcH/W5qfHq/zbA5hBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:08:04.781561Z"},"content_sha256":"097f2b5fc2f6fa9833cd440da126dc19c084697a26e7dcdc4fb4e415bb8a9e05","schema_version":"1.0","event_id":"sha256:097f2b5fc2f6fa9833cd440da126dc19c084697a26e7dcdc4fb4e415bb8a9e05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:V4NHCTIZ7I2NKIH6A2EIKFCZGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ.","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Yaoran Yang, Yutong Zhang","submitted_at":"2026-05-16T14:48:31Z","abstract_excerpt":"A 2024 paper of Sun, Ding and Wang introduced a second class of constacyclic codes over finite fields, denoted $C(q,m,r,\\ell)$, with length $(q^m-1)/r$, where $r\\mid(q-1)$ and the defining monomials have total $q$-ary degree congruent to $r-1$ modulo $r$. In the non-projective intermediate range $2<r<q-1$ the paper gave a sharp-looking upper bound and a BCH-type lower bound, and left the minimum distance open. We prove that the upper bound is the exact minimum distance for every admissible intermediate parameter. More precisely, if $\\ell=(q-1)a+b<(q-1)m-1$, $0\\le b\\le q-2$, and $b\\equiv r-1\\pm"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"If ℓ=(q-1)a+b<(q-1)m-1, 0≤b≤q-2, and b≡r-1 (mod r), then for every prime power q, every divisor r of q-1 with 2<r<q-1, and every m≥2, d(C(q,m,r,ℓ)) equals (q-1)/r *(q-b+1)q^{m-a-2} when 0≤a≤m-2 and (q-b+r-2)/r when a=m-1.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proof relies on the hidden scalar homogeneity of the evaluation model for these codes, which is invoked to enable the orbit-counting obstruction and the homogeneous pencil construction that attain the claimed distances and supports.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"135a079d6792a87e64f193bb555938b5aee11abe12367dd23dcea659372327c9"},"source":{"id":"2605.17022","kind":"arxiv","version":1},"verdict":{"id":"4e34c233-e40b-495f-99ff-d7774903e907","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:33:54.304762Z","strongest_claim":"If ℓ=(q-1)a+b<(q-1)m-1, 0≤b≤q-2, and b≡r-1 (mod r), then for every prime power q, every divisor r of q-1 with 2<r<q-1, and every m≥2, d(C(q,m,r,ℓ)) equals (q-1)/r *(q-b+1)q^{m-a-2} when 0≤a≤m-2 and (q-b+r-2)/r when a=m-1.","one_line_summary":"Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proof relies on the hidden scalar homogeneity of the evaluation model for these codes, which is invoked to enable the orbit-counting obstruction and the homogeneous pencil construction that attain the claimed distances and supports.","pith_extraction_headline":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17022/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"citation_quote_validity","ran_at":"2026-05-19T19:49:46.058775Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.804863Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T18:51:58.434115Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.181805Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:40:41.530310Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:24.856359Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ade3c501d40cd346946d76ece7ce60a2eda15c7d7fd9783322beda07e0068af1"},"references":{"count":19,"sample":[{"doi":"","year":2024,"title":"Two classes of constacyclic codes with variable parameters[(q m −1)/r, k, d],","work_id":"8a2a9126-1bbd-4570-ab43-4dca27ec118f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Two classes of constacyclic codes with a square-root-like lower bound,","work_id":"64f11988-d0e6-401e-8b5e-c0398b3ecff1","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1970,"title":"On generalized Reed–Muller codes and their relatives,","work_id":"d7a4487a-857d-4c32-9b73-10ac8133aa55","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1976,"title":"On the weight enumeration of weights less than2.5dof Reed–Muller codes,","work_id":"8300c54b-68be-4f00-82b6-a5eca9aced35","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1970,"title":"On the weight structure of Reed–Muller codes,","work_id":"cfa5ddd9-ea37-4e8a-9f6d-b82e27e7cb0c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":19,"snapshot_sha256":"7dbd927f8f9519f6f2859ab8a0fb7ddc3b87c1b7b7a45090a3edb3ce9b555160","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"4e34c233-e40b-495f-99ff-d7774903e907"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:03:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciyre92NaXiygnN2HhfBJVmEnmkmERVFx3cL4z9gjdvD8acWqSj3WucWn9xdp7lK3g4JzeohOCSu0im6MAidCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:08:04.783021Z"},"content_sha256":"0377aac1b54eeb234d7d5c4a8f983c54811d43592b16cbf75c2fd666df3ac4b8","schema_version":"1.0","event_id":"sha256:0377aac1b54eeb234d7d5c4a8f983c54811d43592b16cbf75c2fd666df3ac4b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/bundle.json","state_url":"https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T21:08:04Z","links":{"resolver":"https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI","bundle":"https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/bundle.json","state":"https://pith.science/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4NHCTIZ7I2NKIH6A2EIKFCZGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:V4NHCTIZ7I2NKIH6A2EIKFCZGI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3944e428e92576fe038bad3b12febbb6000302cc5e08e9c3249bc2630da26b75","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-16T14:48:31Z","title_canon_sha256":"a7117ec1c018348272685a2541d3a37a65c3f9a98f7d18f0e22b53b0db9b402c"},"schema_version":"1.0","source":{"id":"2605.17022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17022","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17022v1","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17022","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"V4NHCTIZ7I2N","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_16","alias_value":"V4NHCTIZ7I2NKIH6","created_at":"2026-05-20T00:03:36Z"},{"alias_kind":"pith_short_8","alias_value":"V4NHCTIZ","created_at":"2026-05-20T00:03:36Z"}],"graph_snapshots":[{"event_id":"sha256:0377aac1b54eeb234d7d5c4a8f983c54811d43592b16cbf75c2fd666df3ac4b8","target":"graph","created_at":"2026-05-20T00:03:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"If ℓ=(q-1)a+b<(q-1)m-1, 0≤b≤q-2, and b≡r-1 (mod r), then for every prime power q, every divisor r of q-1 with 2<r<q-1, and every m≥2, d(C(q,m,r,ℓ)) equals (q-1)/r *(q-b+1)q^{m-a-2} when 0≤a≤m-2 and (q-b+r-2)/r when a=m-1."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The proof relies on the hidden scalar homogeneity of the evaluation model for these codes, which is invoked to enable the orbit-counting obstruction and the homogeneous pencil construction that attain the claimed distances and supports."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ."}],"snapshot_sha256":"135a079d6792a87e64f193bb555938b5aee11abe12367dd23dcea659372327c9"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T19:49:46.058775Z","status":"completed","version":"0.1.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.804863Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T18:51:58.434115Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.181805Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T18:40:41.530310Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:24.856359Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17022/integrity.json","findings":[],"snapshot_sha256":"ade3c501d40cd346946d76ece7ce60a2eda15c7d7fd9783322beda07e0068af1","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A 2024 paper of Sun, Ding and Wang introduced a second class of constacyclic codes over finite fields, denoted $C(q,m,r,\\ell)$, with length $(q^m-1)/r$, where $r\\mid(q-1)$ and the defining monomials have total $q$-ary degree congruent to $r-1$ modulo $r$. In the non-projective intermediate range $2<r<q-1$ the paper gave a sharp-looking upper bound and a BCH-type lower bound, and left the minimum distance open. We prove that the upper bound is the exact minimum distance for every admissible intermediate parameter. More precisely, if $\\ell=(q-1)a+b<(q-1)m-1$, $0\\le b\\le q-2$, and $b\\equiv r-1\\pm","authors_text":"Yaoran Yang, Yutong Zhang","cross_cats":["math.IT"],"headline":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-16T14:48:31Z","title":"Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers"},"references":{"count":19,"internal_anchors":0,"resolved_work":19,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Two classes of constacyclic codes with variable parameters[(q m −1)/r, k, d],","work_id":"8a2a9126-1bbd-4570-ab43-4dca27ec118f","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Two classes of constacyclic codes with a square-root-like lower bound,","work_id":"64f11988-d0e6-401e-8b5e-c0398b3ecff1","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"On generalized Reed–Muller codes and their relatives,","work_id":"d7a4487a-857d-4c32-9b73-10ac8133aa55","year":1970},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"On the weight enumeration of weights less than2.5dof Reed–Muller codes,","work_id":"8300c54b-68be-4f00-82b6-a5eca9aced35","year":1976},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"On the weight structure of Reed–Muller codes,","work_id":"cfa5ddd9-ea37-4e8a-9f6d-b82e27e7cb0c","year":1970}],"snapshot_sha256":"7dbd927f8f9519f6f2859ab8a0fb7ddc3b87c1b7b7a45090a3edb3ce9b555160"},"source":{"id":"2605.17022","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:33:54.304762Z","id":"4e34c233-e40b-495f-99ff-d7774903e907","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The minimum distance of intermediate constacyclic codes equals an explicit case formula in the field size q and the parameters a and b of the degree ℓ.","strongest_claim":"If ℓ=(q-1)a+b<(q-1)m-1, 0≤b≤q-2, and b≡r-1 (mod r), then for every prime power q, every divisor r of q-1 with 2<r<q-1, and every m≥2, d(C(q,m,r,ℓ)) equals (q-1)/r *(q-b+1)q^{m-a-2} when 0≤a≤m-2 and (q-b+r-2)/r when a=m-1.","weakest_assumption":"The proof relies on the hidden scalar homogeneity of the evaluation model for these codes, which is invoked to enable the orbit-counting obstruction and the homogeneous pencil construction that attain the claimed distances and supports."}},"verdict_id":"4e34c233-e40b-495f-99ff-d7774903e907"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:097f2b5fc2f6fa9833cd440da126dc19c084697a26e7dcdc4fb4e415bb8a9e05","target":"record","created_at":"2026-05-20T00:03:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3944e428e92576fe038bad3b12febbb6000302cc5e08e9c3249bc2630da26b75","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-16T14:48:31Z","title_canon_sha256":"a7117ec1c018348272685a2541d3a37a65c3f9a98f7d18f0e22b53b0db9b402c"},"schema_version":"1.0","source":{"id":"2605.17022","kind":"arxiv","version":1}},"canonical_sha256":"af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af1a714d19fa34d520fe068885145932223275303a479f29a6569add3d10a8c4","first_computed_at":"2026-05-20T00:03:36.414087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:36.414087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9MIPuKhR7vS2dkifGgJ2r04mAVb0sxaVqpjE9nh/arUUgaIxOuV2Nivv/pYcTgNmFB3Re3d0oXdTXMqgcS8PDA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:36.415089Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:097f2b5fc2f6fa9833cd440da126dc19c084697a26e7dcdc4fb4e415bb8a9e05","sha256:0377aac1b54eeb234d7d5c4a8f983c54811d43592b16cbf75c2fd666df3ac4b8"],"state_sha256":"4cdf7a18c9172ac8ee686d95f89f4dcf32eb3c97a510aa3a30df84d6719bc83e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOtmX5DOABbjCq7nluvINb2TAllkdX9X0nqc0wOKVdOaFoWGH6GicSPEIifHUKwzgHbH+1EccdacuKHC1NNoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:08:04.788443Z","bundle_sha256":"a126b6c9f51623df036fc797716cc4d160ba7b397ecfbfc81b90864f188c9a50"}}