{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MRYUBYLEMPPPHDR23FTHWN5RF7","short_pith_number":"pith:MRYUBYLE","canonical_record":{"source":{"id":"2605.16032","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T15:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"a2e1dd1127b9fa043d5f863775129227f19537b338ac58f148dc8b371c05a81c","abstract_canon_sha256":"6aca950624da861a471db57371dbd9558c7d2038b426369f43b2805a1a93c32b"},"schema_version":"1.0"},"canonical_sha256":"647140e16463def38e3ad9667b37b12ff545c000a737157168230c77c64a1de6","source":{"kind":"arxiv","id":"2605.16032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16032","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16032v1","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16032","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"MRYUBYLEMPPP","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_16","alias_value":"MRYUBYLEMPPPHDR2","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_8","alias_value":"MRYUBYLE","created_at":"2026-05-20T00:01:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MRYUBYLEMPPPHDR23FTHWN5RF7","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16032","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T15:07:34Z","cross_cats_sorted":[],"title_canon_sha256":"a2e1dd1127b9fa043d5f863775129227f19537b338ac58f148dc8b371c05a81c","abstract_canon_sha256":"6aca950624da861a471db57371dbd9558c7d2038b426369f43b2805a1a93c32b"},"schema_version":"1.0"},"canonical_sha256":"647140e16463def38e3ad9667b37b12ff545c000a737157168230c77c64a1de6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:50.022269Z","signature_b64":"P3WYX1H+ko2JJdeZ+DjW+thQpl8xqt0xC0gqWLwY1YHvXb9Z2VhM228YGRHAcK2EHzfkc4IsMzgAbBWfW3nWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"647140e16463def38e3ad9667b37b12ff545c000a737157168230c77c64a1de6","last_reissued_at":"2026-05-20T00:01:50.021688Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:50.021688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16032","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":"2026-05-20T00:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioudz5xy+2baya8psjrCl1D0nOTZ1+pLGg/16ktiam8YMh5ICaPS3fG8NKXtWTNuxc74oy1EUK58XuKy0q9CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:26:34.572223Z"},"content_sha256":"c18940578a1602c169a84ca8a37741867d6b5a5ab4bda704c58d60f58a2357b4","schema_version":"1.0","event_id":"sha256:c18940578a1602c169a84ca8a37741867d6b5a5ab4bda704c58d60f58a2357b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MRYUBYLEMPPPHDR23FTHWN5RF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy bases and relational complexity of diagonal type groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Colva M. Roney-Dougal, Hong Yi Huang","submitted_at":"2026-05-15T15:07:34Z","abstract_excerpt":"A base for a subgroup $G$ of $\\mathrm{Sym}(\\Omega)$ is a sequence of elements of $\\Omega$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b(G)$. There is a natural greedy algorithm to compute a base for $G$, and it was conjectured by Cameron in 1999 that there exists an absolute constant $c$ such that if $G$ is primitive then any base returned by this algorithm has size at most $cb(G)$. In this paper we determine the size of every base returned by the greedy algorithm when $G$ is a primitive group of diagonal type, and hence prove Cameron's conjecture for t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We determine the size of every base returned by the greedy algorithm when G is a primitive group of diagonal type, and hence prove Cameron's conjecture for these groups. We prove that if G is primitive of diagonal type then RC(G) ≥ 4, that this lower bound is attained by infinitely many such G, and that the relational complexity of the groups of diagonal type is unbounded.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis relies on the known structural description of primitive diagonal type groups (socle T^k acting on cosets of a diagonal subgroup) and on the fact that the greedy choice can be tracked via the orbits on the product space; if this structural description or the orbit calculations contain an undetected gap, the exact base sizes and the RC lower bound would not follow.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"For primitive diagonal type groups the greedy base sizes are computed exactly, proving Cameron's conjecture, while relational complexity is shown to be at least 4 with no upper bound.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"826ac004653c026c1fcf90e4e6f423310a87dc2374a70ba2d0b772abe6927699"},"source":{"id":"2605.16032","kind":"arxiv","version":1},"verdict":{"id":"8776bfd6-2420-4be7-ba7f-637e2f934efa","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:58:50.233697Z","strongest_claim":"We determine the size of every base returned by the greedy algorithm when G is a primitive group of diagonal type, and hence prove Cameron's conjecture for these groups. We prove that if G is primitive of diagonal type then RC(G) ≥ 4, that this lower bound is attained by infinitely many such G, and that the relational complexity of the groups of diagonal type is unbounded.","one_line_summary":"For primitive diagonal type groups the greedy base sizes are computed exactly, proving Cameron's conjecture, while relational complexity is shown to be at least 4 with no upper bound.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis relies on the known structural description of primitive diagonal type groups (socle T^k acting on cosets of a diagonal subgroup) and on the fact that the greedy choice can be tracked via the orbits on the product space; if this structural description or the orbit calculations contain an undetected gap, the exact base sizes and the RC lower bound would not follow.","pith_extraction_headline":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16032/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.011766Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:10:49.334956Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:41.565680Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.542451Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1dc400e6dd78e1f96c89a0c1eb6efb3f90de8bd18d098fc9ac77f29e07e92576"},"references":{"count":31,"sample":[{"doi":"","year":2024,"title":"M. Anagnostopoulou-Merkouri and T.C. Burness,On the regularity number of a finite group and other base-related invariants, J. Lond. Math. Soc.110(2024), Paper No. e70035, 65 pp","work_id":"444a455d-55e7-44b4-b79b-fc0b8c950b45","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1992,"title":"K.D. Blaha,Minimum bases for permutation groups: the greedy approximation, J. Algorithms13 (1992), no. 2, 297–306","work_id":"5180ffe8-8251-4637-814b-48588399110d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"J.N. Bray, D.F. Holt and C.M. Roney-Dougal,The maximal subgroups of the low-dimensional finite classical groups, Lond. Math. Soc. Lecture Note Ser., vol. 407, Cambridge Univ. Press, Cambridge, 2013","work_id":"6a1ee44f-3fd1-4026-9d61-9c86322c6c30","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"W. Bosma, J. Cannon and C. Playoust,TheMagmaalgebra system I: The user language, J. Symb. Comput.24(1997), 235–265","work_id":"4492b43c-3030-4198-b07e-adf78d32e223","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"S. Brenner, C. del Valle and C.M. Roney-Dougal,Irredundant bases for soluble groups, Bull. Lond. Math. Soc.57(2025), 3013–3023","work_id":"6582883d-b371-4f7e-9f6d-b90af436ed6e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":31,"snapshot_sha256":"c2db939435781545a36aae30151348eecf6a090a960c6ab031d3e2213d948604","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":"8776bfd6-2420-4be7-ba7f-637e2f934efa"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k426k6CqoABNHNf785dnfKm8tG1XO35FpNnFupOppmmx2nkYdLdld55js+6CQ65SZvI8Nbc9QFPfSw5K3+FGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:26:34.573839Z"},"content_sha256":"34ca524ce72ecbddede4b932d36683b604e19008440c64dd671ad36fcdf28951","schema_version":"1.0","event_id":"sha256:34ca524ce72ecbddede4b932d36683b604e19008440c64dd671ad36fcdf28951"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/bundle.json","state_url":"https://pith.science/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/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":"2026-06-10T11:26:34Z","links":{"resolver":"https://pith.science/pith/MRYUBYLEMPPPHDR23FTHWN5RF7","bundle":"https://pith.science/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/bundle.json","state":"https://pith.science/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRYUBYLEMPPPHDR23FTHWN5RF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MRYUBYLEMPPPHDR23FTHWN5RF7","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":"6aca950624da861a471db57371dbd9558c7d2038b426369f43b2805a1a93c32b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T15:07:34Z","title_canon_sha256":"a2e1dd1127b9fa043d5f863775129227f19537b338ac58f148dc8b371c05a81c"},"schema_version":"1.0","source":{"id":"2605.16032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16032","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16032v1","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16032","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"MRYUBYLEMPPP","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_16","alias_value":"MRYUBYLEMPPPHDR2","created_at":"2026-05-20T00:01:50Z"},{"alias_kind":"pith_short_8","alias_value":"MRYUBYLE","created_at":"2026-05-20T00:01:50Z"}],"graph_snapshots":[{"event_id":"sha256:34ca524ce72ecbddede4b932d36683b604e19008440c64dd671ad36fcdf28951","target":"graph","created_at":"2026-05-20T00:01:50Z","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":"We determine the size of every base returned by the greedy algorithm when G is a primitive group of diagonal type, and hence prove Cameron's conjecture for these groups. We prove that if G is primitive of diagonal type then RC(G) ≥ 4, that this lower bound is attained by infinitely many such G, and that the relational complexity of the groups of diagonal type is unbounded."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The analysis relies on the known structural description of primitive diagonal type groups (socle T^k acting on cosets of a diagonal subgroup) and on the fact that the greedy choice can be tracked via the orbits on the product space; if this structural description or the orbit calculations contain an undetected gap, the exact base sizes and the RC lower bound would not follow."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"For primitive diagonal type groups the greedy base sizes are computed exactly, proving Cameron's conjecture, while relational complexity is shown to be at least 4 with no upper bound."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded."}],"snapshot_sha256":"826ac004653c026c1fcf90e4e6f423310a87dc2374a70ba2d0b772abe6927699"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.011766Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T19:10:49.334956Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:41.565680Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.542451Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16032/integrity.json","findings":[],"snapshot_sha256":"1dc400e6dd78e1f96c89a0c1eb6efb3f90de8bd18d098fc9ac77f29e07e92576","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A base for a subgroup $G$ of $\\mathrm{Sym}(\\Omega)$ is a sequence of elements of $\\Omega$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b(G)$. There is a natural greedy algorithm to compute a base for $G$, and it was conjectured by Cameron in 1999 that there exists an absolute constant $c$ such that if $G$ is primitive then any base returned by this algorithm has size at most $cb(G)$. In this paper we determine the size of every base returned by the greedy algorithm when $G$ is a primitive group of diagonal type, and hence prove Cameron's conjecture for t","authors_text":"Colva M. Roney-Dougal, Hong Yi Huang","cross_cats":[],"headline":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T15:07:34Z","title":"Greedy bases and relational complexity of diagonal type groups"},"references":{"count":31,"internal_anchors":0,"resolved_work":31,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"M. Anagnostopoulou-Merkouri and T.C. Burness,On the regularity number of a finite group and other base-related invariants, J. Lond. Math. Soc.110(2024), Paper No. e70035, 65 pp","work_id":"444a455d-55e7-44b4-b79b-fc0b8c950b45","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"K.D. Blaha,Minimum bases for permutation groups: the greedy approximation, J. Algorithms13 (1992), no. 2, 297–306","work_id":"5180ffe8-8251-4637-814b-48588399110d","year":1992},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"J.N. Bray, D.F. Holt and C.M. Roney-Dougal,The maximal subgroups of the low-dimensional finite classical groups, Lond. Math. Soc. Lecture Note Ser., vol. 407, Cambridge Univ. Press, Cambridge, 2013","work_id":"6a1ee44f-3fd1-4026-9d61-9c86322c6c30","year":2013},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"W. Bosma, J. Cannon and C. Playoust,TheMagmaalgebra system I: The user language, J. Symb. Comput.24(1997), 235–265","work_id":"4492b43c-3030-4198-b07e-adf78d32e223","year":1997},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"S. Brenner, C. del Valle and C.M. Roney-Dougal,Irredundant bases for soluble groups, Bull. Lond. Math. Soc.57(2025), 3013–3023","work_id":"6582883d-b371-4f7e-9f6d-b90af436ed6e","year":2025}],"snapshot_sha256":"c2db939435781545a36aae30151348eecf6a090a960c6ab031d3e2213d948604"},"source":{"id":"2605.16032","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:58:50.233697Z","id":"8776bfd6-2420-4be7-ba7f-637e2f934efa","model_set":{"reader":"grok-4.3"},"one_line_summary":"For primitive diagonal type groups the greedy base sizes are computed exactly, proving Cameron's conjecture, while relational complexity is shown to be at least 4 with no upper bound.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Primitive groups of diagonal type satisfy Cameron's conjecture on greedy base sizes and have relational complexity at least 4 that is unbounded.","strongest_claim":"We determine the size of every base returned by the greedy algorithm when G is a primitive group of diagonal type, and hence prove Cameron's conjecture for these groups. We prove that if G is primitive of diagonal type then RC(G) ≥ 4, that this lower bound is attained by infinitely many such G, and that the relational complexity of the groups of diagonal type is unbounded.","weakest_assumption":"The analysis relies on the known structural description of primitive diagonal type groups (socle T^k acting on cosets of a diagonal subgroup) and on the fact that the greedy choice can be tracked via the orbits on the product space; if this structural description or the orbit calculations contain an undetected gap, the exact base sizes and the RC lower bound would not follow."}},"verdict_id":"8776bfd6-2420-4be7-ba7f-637e2f934efa"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c18940578a1602c169a84ca8a37741867d6b5a5ab4bda704c58d60f58a2357b4","target":"record","created_at":"2026-05-20T00:01:50Z","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":"6aca950624da861a471db57371dbd9558c7d2038b426369f43b2805a1a93c32b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T15:07:34Z","title_canon_sha256":"a2e1dd1127b9fa043d5f863775129227f19537b338ac58f148dc8b371c05a81c"},"schema_version":"1.0","source":{"id":"2605.16032","kind":"arxiv","version":1}},"canonical_sha256":"647140e16463def38e3ad9667b37b12ff545c000a737157168230c77c64a1de6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"647140e16463def38e3ad9667b37b12ff545c000a737157168230c77c64a1de6","first_computed_at":"2026-05-20T00:01:50.021688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:50.021688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P3WYX1H+ko2JJdeZ+DjW+thQpl8xqt0xC0gqWLwY1YHvXb9Z2VhM228YGRHAcK2EHzfkc4IsMzgAbBWfW3nWAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:50.022269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c18940578a1602c169a84ca8a37741867d6b5a5ab4bda704c58d60f58a2357b4","sha256:34ca524ce72ecbddede4b932d36683b604e19008440c64dd671ad36fcdf28951"],"state_sha256":"e3a83fe1f0d45f0271617df7499ea6e74c63ce44dea0c0c37d435f1148302b0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYJDL+5tyfNlR2Mgr9l0hgPk1kbhsiIrPm9vvcFpLkabVqSfKVFqR639pOeePsYrKj+9Q/JGJbtszCTArCW2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:26:34.580246Z","bundle_sha256":"64e2d393d9a4aec626d90b7ff82d98d8c5e418363a33a1482e29995605fa8c69"}}