{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OOEVVFLAOGWTRWVH4ESIKIWXYD","short_pith_number":"pith:OOEVVFLA","canonical_record":{"source":{"id":"2507.06225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-07-08T17:58:51Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"e1ae686d9867e802169d6f6eb82e1b65b5f049860b551e5b1a3de2d34232fec3","abstract_canon_sha256":"3b05a1518dc1f96f09140338139307d124aa0f85679949368e4abdb83442f8f6"},"schema_version":"1.0"},"canonical_sha256":"73895a956071ad38daa7e1248522d7c0eaf0a30adf96126d18afd9c651e27768","source":{"kind":"arxiv","id":"2507.06225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06225","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06225v1","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06225","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_12","alias_value":"OOEVVFLAOGWT","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_16","alias_value":"OOEVVFLAOGWTRWVH","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_8","alias_value":"OOEVVFLA","created_at":"2026-07-05T11:33:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OOEVVFLAOGWTRWVH4ESIKIWXYD","target":"record","payload":{"canonical_record":{"source":{"id":"2507.06225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-07-08T17:58:51Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"e1ae686d9867e802169d6f6eb82e1b65b5f049860b551e5b1a3de2d34232fec3","abstract_canon_sha256":"3b05a1518dc1f96f09140338139307d124aa0f85679949368e4abdb83442f8f6"},"schema_version":"1.0"},"canonical_sha256":"73895a956071ad38daa7e1248522d7c0eaf0a30adf96126d18afd9c651e27768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:54.568295Z","signature_b64":"TW110PAScBjU8se3S92zNOu+4tD984zk2YUvLoT6EerjJAo+owx6hAcofMETVSZ+XwkZKzv/56EmQ2i7l1TjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73895a956071ad38daa7e1248522d7c0eaf0a30adf96126d18afd9c651e27768","last_reissued_at":"2026-07-05T11:33:54.567892Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:54.567892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.06225","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":"2026-07-05T11:33:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5c/eL83oIKSpaYYXL/WPNIggqT8elEsxEtQhy/9yuMjDhZSC01xlw2sQiU3hmBhpfli0n/znzT3exhjhnyezCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:56:09.594635Z"},"content_sha256":"235f00c3d8e658eef0a2a3017cb0d980989399dc8d1d94f4a81591110acc3c49","schema_version":"1.0","event_id":"sha256:235f00c3d8e658eef0a2a3017cb0d980989399dc8d1d94f4a81591110acc3c49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OOEVVFLAOGWTRWVH4ESIKIWXYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matroid isomorphism games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.QA","authors_text":"Daniel Corey, Marcel Wack, Simon Schmidt","submitted_at":"2025-07-08T17:58:51Z","abstract_excerpt":"We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the matroids are isomorphic if and only if the game has a perfect classical winning strategy. We define notions of quantum isomorphism in terms of perfect quantum commuting strategies, and we find a pair of nonisomorphic matroids that are quantum isomorphic. We also give a purely algebraic characterization of quantum isomorphic matroids. Finally, we use this notio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06225","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/2507.06225/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":"2026-07-05T11:33:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaEYjA/Wl+6NmW7Ug4JfWgfv97gyARu3EIFIoeyjQdNcqRGKYgdj/kx3kwJHLmOzoD96acR4Tw6agSMnpyldCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:56:09.595627Z"},"content_sha256":"93ac926a932c526d38bdb696e10a892696bdb5df3b472a36a4a4129ba6ec192c","schema_version":"1.0","event_id":"sha256:93ac926a932c526d38bdb696e10a892696bdb5df3b472a36a4a4129ba6ec192c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/bundle.json","state_url":"https://pith.science/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/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":"2026-08-12T22:56:09Z","links":{"resolver":"https://pith.science/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD","bundle":"https://pith.science/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/bundle.json","state":"https://pith.science/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOEVVFLAOGWTRWVH4ESIKIWXYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OOEVVFLAOGWTRWVH4ESIKIWXYD","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":"3b05a1518dc1f96f09140338139307d124aa0f85679949368e4abdb83442f8f6","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-07-08T17:58:51Z","title_canon_sha256":"e1ae686d9867e802169d6f6eb82e1b65b5f049860b551e5b1a3de2d34232fec3"},"schema_version":"1.0","source":{"id":"2507.06225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06225","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06225v1","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06225","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_12","alias_value":"OOEVVFLAOGWT","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_16","alias_value":"OOEVVFLAOGWTRWVH","created_at":"2026-07-05T11:33:54Z"},{"alias_kind":"pith_short_8","alias_value":"OOEVVFLA","created_at":"2026-07-05T11:33:54Z"}],"graph_snapshots":[{"event_id":"sha256:93ac926a932c526d38bdb696e10a892696bdb5df3b472a36a4a4129ba6ec192c","target":"graph","created_at":"2026-07-05T11:33:54Z","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/2507.06225/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the matroids are isomorphic if and only if the game has a perfect classical winning strategy. We define notions of quantum isomorphism in terms of perfect quantum commuting strategies, and we find a pair of nonisomorphic matroids that are quantum isomorphic. We also give a purely algebraic characterization of quantum isomorphic matroids. Finally, we use this notio","authors_text":"Daniel Corey, Marcel Wack, Simon Schmidt","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-07-08T17:58:51Z","title":"Matroid isomorphism games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06225","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":"sha256:235f00c3d8e658eef0a2a3017cb0d980989399dc8d1d94f4a81591110acc3c49","target":"record","created_at":"2026-07-05T11:33:54Z","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":"3b05a1518dc1f96f09140338139307d124aa0f85679949368e4abdb83442f8f6","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-07-08T17:58:51Z","title_canon_sha256":"e1ae686d9867e802169d6f6eb82e1b65b5f049860b551e5b1a3de2d34232fec3"},"schema_version":"1.0","source":{"id":"2507.06225","kind":"arxiv","version":1}},"canonical_sha256":"73895a956071ad38daa7e1248522d7c0eaf0a30adf96126d18afd9c651e27768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73895a956071ad38daa7e1248522d7c0eaf0a30adf96126d18afd9c651e27768","first_computed_at":"2026-07-05T11:33:54.567892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:54.567892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TW110PAScBjU8se3S92zNOu+4tD984zk2YUvLoT6EerjJAo+owx6hAcofMETVSZ+XwkZKzv/56EmQ2i7l1TjAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:54.568295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:235f00c3d8e658eef0a2a3017cb0d980989399dc8d1d94f4a81591110acc3c49","sha256:93ac926a932c526d38bdb696e10a892696bdb5df3b472a36a4a4129ba6ec192c"],"state_sha256":"cacc8862fa0305186c002fc3231204a04e260f52eb5195a0b5806cfd078969c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6NeBAOLsgFNRLInbzQrLsldlF0qeYpR5A7jLrxNd+E/cpnd1z0UMLXx+JBYElW9twLT2QutJweYC/CfbZoqNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:56:09.604294Z","bundle_sha256":"e99d146315f49bc9a7dacb8658a83396273bd686b4813f566281cdc300620f8c"}}