{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D5NY2IF62KG7QXNRGWITAICEFN","short_pith_number":"pith:D5NY2IF6","canonical_record":{"source":{"id":"1005.2300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-13T11:19:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"218e63d14e912a36c08226f4e850522c936239b88851dc90a1aeda25d72ca86c","abstract_canon_sha256":"f904aadd5a916105318836ef61760b9f1b08ae722ac8106f846decb49b6f84ff"},"schema_version":"1.0"},"canonical_sha256":"1f5b8d20bed28df85db135913020442b79588e1c6ad29761ce99b4718a178482","source":{"kind":"arxiv","id":"1005.2300","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2300","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2300v2","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2300","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"D5NY2IF62KG7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5NY2IF62KG7QXNR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5NY2IF6","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D5NY2IF62KG7QXNRGWITAICEFN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-13T11:19:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"218e63d14e912a36c08226f4e850522c936239b88851dc90a1aeda25d72ca86c","abstract_canon_sha256":"f904aadd5a916105318836ef61760b9f1b08ae722ac8106f846decb49b6f84ff"},"schema_version":"1.0"},"canonical_sha256":"1f5b8d20bed28df85db135913020442b79588e1c6ad29761ce99b4718a178482","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:07.542265Z","signature_b64":"3RMTx6ven1zh/qYVR+183FA3zCUBzjb10ikjFCWrTIH+a/xNQAIvdfe8NQAt8XM4ESNQUw1W0l9dB+MJsREmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5b8d20bed28df85db135913020442b79588e1c6ad29761ce99b4718a178482","last_reissued_at":"2026-05-18T02:24:07.541568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:07.541568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2300","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aa0ykAuaCULtsXrDm4MtCls00umUWPE/bUeef+1fB7VpMj29arwUzrmwordnCAWtFQ/uXsc03h0WdaadTGEIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:26:19.023733Z"},"content_sha256":"0acf3f1764b34ef13e2174d1300b404dea032e5e983ea0444ca29dff9078b65d","schema_version":"1.0","event_id":"sha256:0acf3f1764b34ef13e2174d1300b404dea032e5e983ea0444ca29dff9078b65d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D5NY2IF62KG7QXNRGWITAICEFN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of configuration space of two particles on a graph, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Elizabeth Hanbury, Michael Farber","submitted_at":"2010-05-13T11:19:17Z","abstract_excerpt":"This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We introduce a linking bilinear form on the homology group of the graph with values in the cokernel of the intersection form (introduced in Part I of this work). For a large class of graphs, which we call mature graphs, we give explicit expressions for the homology groups of the configuration space. We show that under a simple condition, adding an edge to a matu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2300","kind":"arxiv","version":2},"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":"2026-05-18T02:24:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtY1fEfbq22HvbZDNmGJfNffkw0dwa3E/VzgiO5fvRGYuKcaooX2jBiJn5Nn9aniH32U9eqiGeHGd9lCKZ3yAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:26:19.024487Z"},"content_sha256":"72c43f96b40c45a9ecb3e44a7023c9c0d3197ad75b4391199d1ff8b6b5f3854c","schema_version":"1.0","event_id":"sha256:72c43f96b40c45a9ecb3e44a7023c9c0d3197ad75b4391199d1ff8b6b5f3854c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5NY2IF62KG7QXNRGWITAICEFN/bundle.json","state_url":"https://pith.science/pith/D5NY2IF62KG7QXNRGWITAICEFN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5NY2IF62KG7QXNRGWITAICEFN/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":"2026-06-08T18:26:19Z","links":{"resolver":"https://pith.science/pith/D5NY2IF62KG7QXNRGWITAICEFN","bundle":"https://pith.science/pith/D5NY2IF62KG7QXNRGWITAICEFN/bundle.json","state":"https://pith.science/pith/D5NY2IF62KG7QXNRGWITAICEFN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5NY2IF62KG7QXNRGWITAICEFN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D5NY2IF62KG7QXNRGWITAICEFN","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":"f904aadd5a916105318836ef61760b9f1b08ae722ac8106f846decb49b6f84ff","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-13T11:19:17Z","title_canon_sha256":"218e63d14e912a36c08226f4e850522c936239b88851dc90a1aeda25d72ca86c"},"schema_version":"1.0","source":{"id":"1005.2300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2300","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2300v2","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2300","created_at":"2026-05-18T02:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"D5NY2IF62KG7","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5NY2IF62KG7QXNR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5NY2IF6","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:72c43f96b40c45a9ecb3e44a7023c9c0d3197ad75b4391199d1ff8b6b5f3854c","target":"graph","created_at":"2026-05-18T02:24:07Z","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":"This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We introduce a linking bilinear form on the homology group of the graph with values in the cokernel of the intersection form (introduced in Part I of this work). For a large class of graphs, which we call mature graphs, we give explicit expressions for the homology groups of the configuration space. We show that under a simple condition, adding an edge to a matu","authors_text":"Elizabeth Hanbury, Michael Farber","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-13T11:19:17Z","title":"Topology of configuration space of two particles on a graph, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2300","kind":"arxiv","version":2},"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":"sha256:0acf3f1764b34ef13e2174d1300b404dea032e5e983ea0444ca29dff9078b65d","target":"record","created_at":"2026-05-18T02:24:07Z","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":"f904aadd5a916105318836ef61760b9f1b08ae722ac8106f846decb49b6f84ff","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-05-13T11:19:17Z","title_canon_sha256":"218e63d14e912a36c08226f4e850522c936239b88851dc90a1aeda25d72ca86c"},"schema_version":"1.0","source":{"id":"1005.2300","kind":"arxiv","version":2}},"canonical_sha256":"1f5b8d20bed28df85db135913020442b79588e1c6ad29761ce99b4718a178482","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5b8d20bed28df85db135913020442b79588e1c6ad29761ce99b4718a178482","first_computed_at":"2026-05-18T02:24:07.541568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:07.541568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3RMTx6ven1zh/qYVR+183FA3zCUBzjb10ikjFCWrTIH+a/xNQAIvdfe8NQAt8XM4ESNQUw1W0l9dB+MJsREmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:07.542265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0acf3f1764b34ef13e2174d1300b404dea032e5e983ea0444ca29dff9078b65d","sha256:72c43f96b40c45a9ecb3e44a7023c9c0d3197ad75b4391199d1ff8b6b5f3854c"],"state_sha256":"17218ec36d054686673bd2b0ab2cf368f447444beaf9eada8df42349e358b059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0eYGGUQP9FaLTte8NDR5b7+q+Sa/qV4mnSeXLFgR/WgBhzGHFe5/Eo4TiDBWR8J3DddOcCTkRxksuzcycp/WAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:26:19.029238Z","bundle_sha256":"f6e2fa479b935890b6ea01958569b69481c4b0d854ee6ea5b01de47322bd6035"}}