{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JXLQV6BQHRZ7UR6LR7MTYUY5UI","short_pith_number":"pith:JXLQV6BQ","canonical_record":{"source":{"id":"2605.17544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"69d4552ae27b17349f72787bedea74a498166cfd3e57204f08e1e33db82cdd5b","abstract_canon_sha256":"b09181ca65146bca4046a50cc93cde7473f11a9bbf02c5a2925e83b65c1497c2"},"schema_version":"1.0"},"canonical_sha256":"4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77","source":{"kind":"arxiv","id":"2605.17544","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17544","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17544v1","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17544","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"JXLQV6BQHRZ7","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"JXLQV6BQHRZ7UR6L","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"JXLQV6BQ","created_at":"2026-05-20T00:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JXLQV6BQHRZ7UR6LR7MTYUY5UI","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"69d4552ae27b17349f72787bedea74a498166cfd3e57204f08e1e33db82cdd5b","abstract_canon_sha256":"b09181ca65146bca4046a50cc93cde7473f11a9bbf02c5a2925e83b65c1497c2"},"schema_version":"1.0"},"canonical_sha256":"4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:45.043153Z","signature_b64":"PdsO6BCtqu/43ivX+JlhdSLeSixYNpchLIPR24p0GcnPMPc4yGdQnJchhX10ZEdsbc0dJ+C8RMCZRSNTUxokAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77","last_reissued_at":"2026-05-20T00:04:45.042193Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:45.042193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17544","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":"2026-05-20T00:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBvwuZm0hbIFkSEshC15hvFFO2lz5OS0LoEJwf5ZGCSNnyy7wW8jpa1GZOcyHxzVvDYicZo/EX7O6tcTCKmzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:52:08.907236Z"},"content_sha256":"ae9a7bc9f6739225f14e3ca8b4b8c4dc8bc3ee21a50e06d6f6658c64a2e1c360","schema_version":"1.0","event_id":"sha256:ae9a7bc9f6739225f14e3ca8b4b8c4dc8bc3ee21a50e06d6f6658c64a2e1c360"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JXLQV6BQHRZ7UR6LR7MTYUY5UI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Generic Linearly Constrained Frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Nixon, Hakan Guler, Zakir Deniz","submitted_at":"2026-05-17T16:53:49Z","abstract_excerpt":"A linearly constrained framework in $\\mathbb{R}^d$ is a bar-joint framework where, in addition, vertices with loops are constrained to lie in given affine subspaces. In the generic case, when each vertex is incident to sufficiently many loops, a characterisation of rigidity was obtained by Jackson, Nixon and Tanigawa for all $d\\geq 3$. By extending this to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in $\\mathbb{R}^d$ are obtained. In the 2-dimensional case ge"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By extending the characterisation of rigidity to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in R^d are obtained.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The generic case assumption together with the hypothesis that each vertex is incident to sufficiently many loops, which is required for the prior rigidity characterisation by Jackson, Nixon and Tanigawa to extend to the matroid rank function.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends rigidity characterizations for linearly constrained generic frameworks to the matroid rank function and obtains sufficient conditions for global rigidity in R^d, with a sharper 2D result via discharging.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d36e9c6d1409ead9fd6f28dc0654f79704e49debaf07df27b941441fa1f97695"},"source":{"id":"2605.17544","kind":"arxiv","version":1},"verdict":{"id":"01685967-6a4c-4df9-b45b-effb9a67e982","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:17:38.439144Z","strongest_claim":"By extending the characterisation of rigidity to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in R^d are obtained.","one_line_summary":"Extends rigidity characterizations for linearly constrained generic frameworks to the matroid rank function and obtains sufficient conditions for global rigidity in R^d, with a sharper 2D result via discharging.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The generic case assumption together with the hypothesis that each vertex is incident to sufficiently many loops, which is required for the prior rigidity characterisation by Jackson, Nixon and Tanigawa to extend to the matroid rank function.","pith_extraction_headline":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17544/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.592745Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:07.055066Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.611020Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.546461Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"aaf8f2b073b343e3c9c8a0d9ecd8fdf9d7a3fbe679125f265977473e34519dad"},"references":{"count":20,"sample":[{"doi":"","year":2008,"title":"Abbot, Generalizations of Kempe’s Universality Theorem","work_id":"43073738-6064-48ac-961c-f7c700d69b5f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"D. Antolini, S. Dewar and S.-I. Tanigawa, Dilworth truncations and Hadamard products of linear spaces to appear in: SIAM Journal on Disc. Math., https://arxiv.org/pdf/2508.04798","work_id":"83ae6775-bdcf-41b9-8bf6-0ea7beb50245","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1978,"title":"L. Asimow and B. Roth, The rigidity of graphs, Trans. Am. Math. Soc. 245 (1978), 279-289","work_id":"826aef49-78f2-4a7e-9c5a-207d03f005bd","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"J. Cruickshank, H. Guler, B. Jackson and A. Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices 12 (2020), 3824–3840","work_id":"510012b9-a9f9-4db5-a54c-14a669c692fc","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"J. Cruickshank, F. Mohammadi, H. J. Motwani, A. Nixon, and S.-I. Tanigawa, Global Rigidity of Line Constrained Frameworks, SIAM Journal on Disc. Math. 38 (2024), 743-763","work_id":"10005033-a542-4c8b-a8ac-1b1fe246ab34","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":20,"snapshot_sha256":"1889d9083058c17be51c6ba5c3957e481950a4c4845c3ea87119cf72fb8d9f41","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":"01685967-6a4c-4df9-b45b-effb9a67e982"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V8v9RxSw1nKhZYh2usG5QpILd09m4RADuoLKyNfxJCneoDZCcNDCcVfzzgeHMAi+VWfhXQ7qWEmlDNHRzEMWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:52:08.907939Z"},"content_sha256":"41d86f3228107cb3619e6f9230a111db8291beba42ce8a3ede37bff5ac0ae0c9","schema_version":"1.0","event_id":"sha256:41d86f3228107cb3619e6f9230a111db8291beba42ce8a3ede37bff5ac0ae0c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/bundle.json","state_url":"https://pith.science/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/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":"2026-06-08T21:52:08Z","links":{"resolver":"https://pith.science/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI","bundle":"https://pith.science/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/bundle.json","state":"https://pith.science/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXLQV6BQHRZ7UR6LR7MTYUY5UI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JXLQV6BQHRZ7UR6LR7MTYUY5UI","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":"b09181ca65146bca4046a50cc93cde7473f11a9bbf02c5a2925e83b65c1497c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:53:49Z","title_canon_sha256":"69d4552ae27b17349f72787bedea74a498166cfd3e57204f08e1e33db82cdd5b"},"schema_version":"1.0","source":{"id":"2605.17544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17544","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17544v1","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17544","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"JXLQV6BQHRZ7","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"JXLQV6BQHRZ7UR6L","created_at":"2026-05-20T00:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"JXLQV6BQ","created_at":"2026-05-20T00:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:41d86f3228107cb3619e6f9230a111db8291beba42ce8a3ede37bff5ac0ae0c9","target":"graph","created_at":"2026-05-20T00:04:45Z","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":"By extending the characterisation of rigidity to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in R^d are obtained."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The generic case assumption together with the hypothesis that each vertex is incident to sufficiently many loops, which is required for the prior rigidity characterisation by Jackson, Nixon and Tanigawa to extend to the matroid rank function."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Extends rigidity characterizations for linearly constrained generic frameworks to the matroid rank function and obtains sufficient conditions for global rigidity in R^d, with a sharper 2D result via discharging."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension."}],"snapshot_sha256":"d36e9c6d1409ead9fd6f28dc0654f79704e49debaf07df27b941441fa1f97695"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.592745Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:31:07.055066Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.611020Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.546461Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17544/integrity.json","findings":[],"snapshot_sha256":"aaf8f2b073b343e3c9c8a0d9ecd8fdf9d7a3fbe679125f265977473e34519dad","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A linearly constrained framework in $\\mathbb{R}^d$ is a bar-joint framework where, in addition, vertices with loops are constrained to lie in given affine subspaces. In the generic case, when each vertex is incident to sufficiently many loops, a characterisation of rigidity was obtained by Jackson, Nixon and Tanigawa for all $d\\geq 3$. By extending this to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in $\\mathbb{R}^d$ are obtained. In the 2-dimensional case ge","authors_text":"Anthony Nixon, Hakan Guler, Zakir Deniz","cross_cats":[],"headline":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:53:49Z","title":"On Generic Linearly Constrained Frameworks"},"references":{"count":20,"internal_anchors":0,"resolved_work":20,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Abbot, Generalizations of Kempe’s Universality Theorem","work_id":"43073738-6064-48ac-961c-f7c700d69b5f","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"D. Antolini, S. Dewar and S.-I. Tanigawa, Dilworth truncations and Hadamard products of linear spaces to appear in: SIAM Journal on Disc. Math., https://arxiv.org/pdf/2508.04798","work_id":"83ae6775-bdcf-41b9-8bf6-0ea7beb50245","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"L. Asimow and B. Roth, The rigidity of graphs, Trans. Am. Math. Soc. 245 (1978), 279-289","work_id":"826aef49-78f2-4a7e-9c5a-207d03f005bd","year":1978},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"J. Cruickshank, H. Guler, B. Jackson and A. Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices 12 (2020), 3824–3840","work_id":"510012b9-a9f9-4db5-a54c-14a669c692fc","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"J. Cruickshank, F. Mohammadi, H. J. Motwani, A. Nixon, and S.-I. Tanigawa, Global Rigidity of Line Constrained Frameworks, SIAM Journal on Disc. Math. 38 (2024), 743-763","work_id":"10005033-a542-4c8b-a8ac-1b1fe246ab34","year":2024}],"snapshot_sha256":"1889d9083058c17be51c6ba5c3957e481950a4c4845c3ea87119cf72fb8d9f41"},"source":{"id":"2605.17544","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:17:38.439144Z","id":"01685967-6a4c-4df9-b45b-effb9a67e982","model_set":{"reader":"grok-4.3"},"one_line_summary":"Extends rigidity characterizations for linearly constrained generic frameworks to the matroid rank function and obtains sufficient conditions for global rigidity in R^d, with a sharper 2D result via discharging.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Extending rigidity characterizations to matroid rank functions provides sufficient conditions for global rigidity of looped simple graphs in any dimension.","strongest_claim":"By extending the characterisation of rigidity to characterise the rank function of the linearly constrained rigidity matroid (under the same loop hypothesis), sufficient conditions for a looped simple graph to be (globally) rigid in R^d are obtained.","weakest_assumption":"The generic case assumption together with the hypothesis that each vertex is incident to sufficiently many loops, which is required for the prior rigidity characterisation by Jackson, Nixon and Tanigawa to extend to the matroid rank function."}},"verdict_id":"01685967-6a4c-4df9-b45b-effb9a67e982"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ae9a7bc9f6739225f14e3ca8b4b8c4dc8bc3ee21a50e06d6f6658c64a2e1c360","target":"record","created_at":"2026-05-20T00:04:45Z","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":"b09181ca65146bca4046a50cc93cde7473f11a9bbf02c5a2925e83b65c1497c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:53:49Z","title_canon_sha256":"69d4552ae27b17349f72787bedea74a498166cfd3e57204f08e1e33db82cdd5b"},"schema_version":"1.0","source":{"id":"2605.17544","kind":"arxiv","version":1}},"canonical_sha256":"4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dd70af8303c73fa47cb8fd93c531da23792fdf04f8553afecdd7e4b2b114e77","first_computed_at":"2026-05-20T00:04:45.042193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:45.042193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PdsO6BCtqu/43ivX+JlhdSLeSixYNpchLIPR24p0GcnPMPc4yGdQnJchhX10ZEdsbc0dJ+C8RMCZRSNTUxokAA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:45.043153Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae9a7bc9f6739225f14e3ca8b4b8c4dc8bc3ee21a50e06d6f6658c64a2e1c360","sha256:41d86f3228107cb3619e6f9230a111db8291beba42ce8a3ede37bff5ac0ae0c9"],"state_sha256":"15d9a2bb67553ddea73933e3a48488ebcc1c5238737c1afadf5dbfdebe24ce0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"133QGtqHRLkuqc+9nZ2m31BVa33/HiFo0ReP9wevvEQxswvBckgXNlhe0pmZvkRX/1PxzH28QwqBTRjYn16+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:52:08.910526Z","bundle_sha256":"7b0f91e454002d9d1f689203f0b9d37210cd8be6a00a7dd6444632cd1d0f58cb"}}