{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SFXPUKH6QKPW4SZAYRPVXM3FYL","short_pith_number":"pith:SFXPUKH6","canonical_record":{"source":{"id":"2605.20409","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T19:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"5569c078be610aabe71af6c862c69fcd9c3318cd1ed9690b00e58ce6499d1221","abstract_canon_sha256":"c8d7bc029d2d6174745b613dc6110bf93cb30dc69bc5cf73a29328d57bb63923"},"schema_version":"1.0"},"canonical_sha256":"916efa28fe829f6e4b20c45f5bb365c2c6ab66b8f2805aff0f16e7435323fed4","source":{"kind":"arxiv","id":"2605.20409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20409","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20409v1","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20409","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"SFXPUKH6QKPW","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_16","alias_value":"SFXPUKH6QKPW4SZA","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_8","alias_value":"SFXPUKH6","created_at":"2026-05-21T01:04:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SFXPUKH6QKPW4SZAYRPVXM3FYL","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20409","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T19:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"5569c078be610aabe71af6c862c69fcd9c3318cd1ed9690b00e58ce6499d1221","abstract_canon_sha256":"c8d7bc029d2d6174745b613dc6110bf93cb30dc69bc5cf73a29328d57bb63923"},"schema_version":"1.0"},"canonical_sha256":"916efa28fe829f6e4b20c45f5bb365c2c6ab66b8f2805aff0f16e7435323fed4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:36.888380Z","signature_b64":"Ayt4/qKRTrDMPM1wNFsH8PQZAvQ+1pDCWXW0t4lsABTQ6HxcUqlidhS9PdZQ9ngGxjwlV0KsIHIg9EXbCG2ZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"916efa28fe829f6e4b20c45f5bb365c2c6ab66b8f2805aff0f16e7435323fed4","last_reissued_at":"2026-05-21T01:04:36.887933Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:36.887933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20409","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":"2026-05-21T01:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eEeZG/f55Upda9/lPr6hNW6qRulGF6scKXncrf3U1Nrk69noLcKAHPp0/8Sl4Zhnn2X2XSqyhQtv0CwaN2p5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:14:10.410493Z"},"content_sha256":"e1f6e4be0c0ed9f1b948cf439d9c72a88ed868302f2a8ad994b844f2a845567f","schema_version":"1.0","event_id":"sha256:e1f6e4be0c0ed9f1b948cf439d9c72a88ed868302f2a8ad994b844f2a845567f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SFXPUKH6QKPW4SZAYRPVXM3FYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher cosystoles of matroids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elana Israel, James Dylan Douthitt, Lee Kennard","submitted_at":"2026-05-19T19:04:53Z","abstract_excerpt":"We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20409","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20409/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzH2ga8ItSEkuN2Xkza3f50/I///SDzk7XU3HFlPoTXNzx1gX1MiUgBK5ADbEIlnI5dFcj6FZTGtEkN1aR9EBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:14:10.411243Z"},"content_sha256":"2c307623a1cd8f04048ae119caf41f7fd71de00bc174c1636461756e70c69ce5","schema_version":"1.0","event_id":"sha256:2c307623a1cd8f04048ae119caf41f7fd71de00bc174c1636461756e70c69ce5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/bundle.json","state_url":"https://pith.science/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/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":"2026-05-25T20:14:10Z","links":{"resolver":"https://pith.science/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL","bundle":"https://pith.science/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/bundle.json","state":"https://pith.science/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFXPUKH6QKPW4SZAYRPVXM3FYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SFXPUKH6QKPW4SZAYRPVXM3FYL","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":"c8d7bc029d2d6174745b613dc6110bf93cb30dc69bc5cf73a29328d57bb63923","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T19:04:53Z","title_canon_sha256":"5569c078be610aabe71af6c862c69fcd9c3318cd1ed9690b00e58ce6499d1221"},"schema_version":"1.0","source":{"id":"2605.20409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20409","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20409v1","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20409","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"SFXPUKH6QKPW","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_16","alias_value":"SFXPUKH6QKPW4SZA","created_at":"2026-05-21T01:04:36Z"},{"alias_kind":"pith_short_8","alias_value":"SFXPUKH6","created_at":"2026-05-21T01:04:36Z"}],"graph_snapshots":[{"event_id":"sha256:2c307623a1cd8f04048ae119caf41f7fd71de00bc174c1636461756e70c69ce5","target":"graph","created_at":"2026-05-21T01:04:36Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class of regular matroids of rank at most six. To accomplish this, we show that it is increasing under matroid extensions and then estimate it for each of the maximal simple regular matroids of rank at most six.","authors_text":"Elana Israel, James Dylan Douthitt, Lee Kennard","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T19:04:53Z","title":"Higher cosystoles of matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20409","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e1f6e4be0c0ed9f1b948cf439d9c72a88ed868302f2a8ad994b844f2a845567f","target":"record","created_at":"2026-05-21T01:04:36Z","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":"c8d7bc029d2d6174745b613dc6110bf93cb30dc69bc5cf73a29328d57bb63923","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T19:04:53Z","title_canon_sha256":"5569c078be610aabe71af6c862c69fcd9c3318cd1ed9690b00e58ce6499d1221"},"schema_version":"1.0","source":{"id":"2605.20409","kind":"arxiv","version":1}},"canonical_sha256":"916efa28fe829f6e4b20c45f5bb365c2c6ab66b8f2805aff0f16e7435323fed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"916efa28fe829f6e4b20c45f5bb365c2c6ab66b8f2805aff0f16e7435323fed4","first_computed_at":"2026-05-21T01:04:36.887933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:36.887933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ayt4/qKRTrDMPM1wNFsH8PQZAvQ+1pDCWXW0t4lsABTQ6HxcUqlidhS9PdZQ9ngGxjwlV0KsIHIg9EXbCG2ZBA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:36.888380Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1f6e4be0c0ed9f1b948cf439d9c72a88ed868302f2a8ad994b844f2a845567f","sha256:2c307623a1cd8f04048ae119caf41f7fd71de00bc174c1636461756e70c69ce5"],"state_sha256":"3e0b1161e4a8bc709ba725b085a868b6177af533678d6a2e73940a485b827aec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKLcqbblN3ABv3biiYhsLWdO1JK6WNpHnqpQBiVfIL8Qaxhaibdd/dyMfAzo0UyjASfJNihQiZPmk+ii9rErAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:14:10.414675Z","bundle_sha256":"6b253ab5734b1449e7b913af3ab77df41c53924c7939c7413e5aafde47feb867"}}