{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WOL664Z2NRI2X453X5TZMP2GYL","short_pith_number":"pith:WOL664Z2","canonical_record":{"source":{"id":"1503.01048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-03T18:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"701aa0e9aef77978f0eec4e5f4c582898bc7ba93dfc061c04d19fe63c6c621a5","abstract_canon_sha256":"02217e555fc059dee1d68431abdccff0ec0900db5cd87c8615e3d10573439887"},"schema_version":"1.0"},"canonical_sha256":"b397ef733a6c51abf3bbbf67963f46c2e9128955def9cd05123190eea9b95bef","source":{"kind":"arxiv","id":"1503.01048","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01048","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01048v1","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01048","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"WOL664Z2NRI2","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WOL664Z2NRI2X453","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WOL664Z2","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WOL664Z2NRI2X453X5TZMP2GYL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-03T18:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"701aa0e9aef77978f0eec4e5f4c582898bc7ba93dfc061c04d19fe63c6c621a5","abstract_canon_sha256":"02217e555fc059dee1d68431abdccff0ec0900db5cd87c8615e3d10573439887"},"schema_version":"1.0"},"canonical_sha256":"b397ef733a6c51abf3bbbf67963f46c2e9128955def9cd05123190eea9b95bef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:47.828485Z","signature_b64":"/Ah/TgJEWnFoTipZFuuSr9a+3u37SSRn4p/RGJlqHvRa3WrV0pzFd2YgI6nsVhb0nYeSGkOV8+TmqYaE2q5tCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b397ef733a6c51abf3bbbf67963f46c2e9128955def9cd05123190eea9b95bef","last_reissued_at":"2026-05-18T02:25:47.827802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:47.827802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01048","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":"2026-05-18T02:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znmN4QZPqhiiEtYni3TRMOaQTbYo2gRibyaNdgQ3GiiTqxPyY6bhIcrDWj89thKeHMR6+mTmsK6JccfJUchyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:21:12.366668Z"},"content_sha256":"d4ba9f345f9d0d7575547e8f91d434db37252dc44a4379059999427a88d7099f","schema_version":"1.0","event_id":"sha256:d4ba9f345f9d0d7575547e8f91d434db37252dc44a4379059999427a88d7099f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WOL664Z2NRI2X453X5TZMP2GYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2-Swappability and the Edge-Reconstruction Number of Regular Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael S. Ross","submitted_at":"2015-03-03T18:43:34Z","abstract_excerpt":"The edge-reconstruction number of graph $G$, denoted $ern(G)$,is the size of the smallest multiset of edge-deleted, unlabeled subgraphs of $G$, from which the structure of $G$ can be uniquely determined. That there was some connection between the areas of edge reconstruction and swappability has been known since the swapping number of a graph was first introduced by Froncek, Rosenberg, and Hlavacek in 2013. This paper illustrates the depth of that connection by proving several bridging results between those areas; in particular, when the graphs in question are both regular and 2-swappable. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01048","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":"2026-05-18T02:25:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNEuR4TQKqc7U5HWPRVMS4l8xOm7WJAUlhojC2DfeRcID117J9ptXsCgv7ET9vrQvMj4WalvLXJ6idldbe1tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:21:12.367249Z"},"content_sha256":"d0bfaafe2feca8dfb13dbda85b52ccc87b244a4d4b770bfbd9380bde7b68ff67","schema_version":"1.0","event_id":"sha256:d0bfaafe2feca8dfb13dbda85b52ccc87b244a4d4b770bfbd9380bde7b68ff67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WOL664Z2NRI2X453X5TZMP2GYL/bundle.json","state_url":"https://pith.science/pith/WOL664Z2NRI2X453X5TZMP2GYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WOL664Z2NRI2X453X5TZMP2GYL/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":"2026-06-07T04:21:12Z","links":{"resolver":"https://pith.science/pith/WOL664Z2NRI2X453X5TZMP2GYL","bundle":"https://pith.science/pith/WOL664Z2NRI2X453X5TZMP2GYL/bundle.json","state":"https://pith.science/pith/WOL664Z2NRI2X453X5TZMP2GYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WOL664Z2NRI2X453X5TZMP2GYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WOL664Z2NRI2X453X5TZMP2GYL","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":"02217e555fc059dee1d68431abdccff0ec0900db5cd87c8615e3d10573439887","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-03T18:43:34Z","title_canon_sha256":"701aa0e9aef77978f0eec4e5f4c582898bc7ba93dfc061c04d19fe63c6c621a5"},"schema_version":"1.0","source":{"id":"1503.01048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01048","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01048v1","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01048","created_at":"2026-05-18T02:25:47Z"},{"alias_kind":"pith_short_12","alias_value":"WOL664Z2NRI2","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WOL664Z2NRI2X453","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WOL664Z2","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:d0bfaafe2feca8dfb13dbda85b52ccc87b244a4d4b770bfbd9380bde7b68ff67","target":"graph","created_at":"2026-05-18T02:25:47Z","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":"The edge-reconstruction number of graph $G$, denoted $ern(G)$,is the size of the smallest multiset of edge-deleted, unlabeled subgraphs of $G$, from which the structure of $G$ can be uniquely determined. That there was some connection between the areas of edge reconstruction and swappability has been known since the swapping number of a graph was first introduced by Froncek, Rosenberg, and Hlavacek in 2013. This paper illustrates the depth of that connection by proving several bridging results between those areas; in particular, when the graphs in question are both regular and 2-swappable. The","authors_text":"Michael S. Ross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-03T18:43:34Z","title":"2-Swappability and the Edge-Reconstruction Number of Regular Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01048","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:d4ba9f345f9d0d7575547e8f91d434db37252dc44a4379059999427a88d7099f","target":"record","created_at":"2026-05-18T02:25:47Z","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":"02217e555fc059dee1d68431abdccff0ec0900db5cd87c8615e3d10573439887","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-03T18:43:34Z","title_canon_sha256":"701aa0e9aef77978f0eec4e5f4c582898bc7ba93dfc061c04d19fe63c6c621a5"},"schema_version":"1.0","source":{"id":"1503.01048","kind":"arxiv","version":1}},"canonical_sha256":"b397ef733a6c51abf3bbbf67963f46c2e9128955def9cd05123190eea9b95bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b397ef733a6c51abf3bbbf67963f46c2e9128955def9cd05123190eea9b95bef","first_computed_at":"2026-05-18T02:25:47.827802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:47.827802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Ah/TgJEWnFoTipZFuuSr9a+3u37SSRn4p/RGJlqHvRa3WrV0pzFd2YgI6nsVhb0nYeSGkOV8+TmqYaE2q5tCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:47.828485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4ba9f345f9d0d7575547e8f91d434db37252dc44a4379059999427a88d7099f","sha256:d0bfaafe2feca8dfb13dbda85b52ccc87b244a4d4b770bfbd9380bde7b68ff67"],"state_sha256":"e809153ae408a2bb168884ededd27193ce6ca58575d5a714c94a4aac465da274"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+5Qntyjd7P77u4L5x4Tgk+KGvilVDze2c81KUvGe7wp+lzzx2tILoHbfq0rEZv329d4Rh8agSo4y9c4mb2GDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:21:12.370620Z","bundle_sha256":"4ca89b75423609ed4346dcb19f66be07a348aa4fbddf949e960ee6f64d8f1fb1"}}