{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:U7IITFKYKYBQMIIAP2IVUJ3U3Y","short_pith_number":"pith:U7IITFKY","canonical_record":{"source":{"id":"1710.10524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T20:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"b2d2b8e68e22925425c4753e4de95dd8ffb1c0a28c2c9870fdfa4b0aaed3b964","abstract_canon_sha256":"948a665e48eeb0bf3b77350837abf61aef79f9e82b7d60b45de1f53dbfd80408"},"schema_version":"1.0"},"canonical_sha256":"a7d089955856030621007e915a2774de03c6d84e045bd08ec3b7f89461386166","source":{"kind":"arxiv","id":"1710.10524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10524","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10524v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10524","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"U7IITFKYKYBQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U7IITFKYKYBQMIIA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U7IITFKY","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:U7IITFKYKYBQMIIAP2IVUJ3U3Y","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T20:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"b2d2b8e68e22925425c4753e4de95dd8ffb1c0a28c2c9870fdfa4b0aaed3b964","abstract_canon_sha256":"948a665e48eeb0bf3b77350837abf61aef79f9e82b7d60b45de1f53dbfd80408"},"schema_version":"1.0"},"canonical_sha256":"a7d089955856030621007e915a2774de03c6d84e045bd08ec3b7f89461386166","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:49.283714Z","signature_b64":"KYcUOFUmc41Uda/ch6RqLLNXaA3CtncDPis3sfmNH4cgNna679VN7R9B6bpnwoBPefJ8dmgY242JCQPLI+15Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7d089955856030621007e915a2774de03c6d84e045bd08ec3b7f89461386166","last_reissued_at":"2026-05-18T00:31:49.283024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:49.283024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10524","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fmf7m1saoynVBa2q6O/bO7PuNXVvKnrP6qgsoFRq7p17S2zlUvivZnsnWBnrRfx2gQNVmA9CYYIcGSa0/Aj0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:29:35.941019Z"},"content_sha256":"0f6d4b020b3dea11fdc20b00521317b10b6580b02b8a8a4945ebfcf27ff42381","schema_version":"1.0","event_id":"sha256:0f6d4b020b3dea11fdc20b00521317b10b6580b02b8a8a4945ebfcf27ff42381"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:U7IITFKYKYBQMIIAP2IVUJ3U3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interlacement and Activities in Delta-Matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ada Morse","submitted_at":"2017-10-28T20:06:14Z","abstract_excerpt":"We generalize theories of graph, matroid, and ribbon-graph activities to delta-matroids. As a result, we obtain an activities based feasible-set expansion for a transition polynomial of delta-matroids defined by Brijder and Hoogeboom. This result yields feasible-set expansions for the two-variable Bollob\\'{a}s-Riordan and interlace polynomials of a delta-matroid. In the former case, the expansion obtained directly generalizes the activities expansions of the Tutte polynomial of graphs and matroids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10524","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":""},"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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3qA6tieKpeNpTmtiqnkq3m5QfhBq3f3V+lQ3jV3Z6tPuHfUncnfB23QjznpUmmsAxrEzqiMwnr9lIOywbm5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:29:35.941360Z"},"content_sha256":"6820a179987710ee045d910a98d5c11387917bc98685d4977d8cd49fa284a33e","schema_version":"1.0","event_id":"sha256:6820a179987710ee045d910a98d5c11387917bc98685d4977d8cd49fa284a33e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/bundle.json","state_url":"https://pith.science/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/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":"2026-06-25T12:29:35Z","links":{"resolver":"https://pith.science/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y","bundle":"https://pith.science/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/bundle.json","state":"https://pith.science/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7IITFKYKYBQMIIAP2IVUJ3U3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:U7IITFKYKYBQMIIAP2IVUJ3U3Y","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":"948a665e48eeb0bf3b77350837abf61aef79f9e82b7d60b45de1f53dbfd80408","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T20:06:14Z","title_canon_sha256":"b2d2b8e68e22925425c4753e4de95dd8ffb1c0a28c2c9870fdfa4b0aaed3b964"},"schema_version":"1.0","source":{"id":"1710.10524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10524","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10524v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10524","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"U7IITFKYKYBQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U7IITFKYKYBQMIIA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U7IITFKY","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:6820a179987710ee045d910a98d5c11387917bc98685d4977d8cd49fa284a33e","target":"graph","created_at":"2026-05-18T00:31:49Z","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"},"paper":{"abstract_excerpt":"We generalize theories of graph, matroid, and ribbon-graph activities to delta-matroids. As a result, we obtain an activities based feasible-set expansion for a transition polynomial of delta-matroids defined by Brijder and Hoogeboom. This result yields feasible-set expansions for the two-variable Bollob\\'{a}s-Riordan and interlace polynomials of a delta-matroid. In the former case, the expansion obtained directly generalizes the activities expansions of the Tutte polynomial of graphs and matroids.","authors_text":"Ada Morse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T20:06:14Z","title":"Interlacement and Activities in Delta-Matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10524","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":"sha256:0f6d4b020b3dea11fdc20b00521317b10b6580b02b8a8a4945ebfcf27ff42381","target":"record","created_at":"2026-05-18T00:31:49Z","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":"948a665e48eeb0bf3b77350837abf61aef79f9e82b7d60b45de1f53dbfd80408","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-28T20:06:14Z","title_canon_sha256":"b2d2b8e68e22925425c4753e4de95dd8ffb1c0a28c2c9870fdfa4b0aaed3b964"},"schema_version":"1.0","source":{"id":"1710.10524","kind":"arxiv","version":1}},"canonical_sha256":"a7d089955856030621007e915a2774de03c6d84e045bd08ec3b7f89461386166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7d089955856030621007e915a2774de03c6d84e045bd08ec3b7f89461386166","first_computed_at":"2026-05-18T00:31:49.283024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:49.283024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYcUOFUmc41Uda/ch6RqLLNXaA3CtncDPis3sfmNH4cgNna679VN7R9B6bpnwoBPefJ8dmgY242JCQPLI+15Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:49.283714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6d4b020b3dea11fdc20b00521317b10b6580b02b8a8a4945ebfcf27ff42381","sha256:6820a179987710ee045d910a98d5c11387917bc98685d4977d8cd49fa284a33e"],"state_sha256":"23bd5c4cc436cc0433a420bd2a1ea28a5ce3faac77b5c8734cda079fdb06efc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hd1seMJ6xjOmnGnyAhmN/QorPqk0vtBLsEnuZPIhpgj64x+z3+ID0LXyBdf2SEhNpM/Hcu44WM3KnY1LLaEfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:29:35.943431Z","bundle_sha256":"84695ec9e154ac066eaa5134f55ffc80fa575c535f7d61047f4ad4aec2beb18f"}}