{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IFO4WS4YJVODYMPNKSBQALL4YK","short_pith_number":"pith:IFO4WS4Y","canonical_record":{"source":{"id":"1303.6799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-03-27T12:10:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3676a6904744c0f64f5b3aeef950acdea0f2cb9c8f464fe4cccb4e40b9f1d52b","abstract_canon_sha256":"92385a6b6f20ebdc273de493b26e4b7f11b6d861ffb11e271ddf96f364ee665e"},"schema_version":"1.0"},"canonical_sha256":"415dcb4b984d5c3c31ed5483002d7cc297305839ea6e7dffd6b7a30c91dd0468","source":{"kind":"arxiv","id":"1303.6799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6799","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6799v1","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6799","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"IFO4WS4YJVOD","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IFO4WS4YJVODYMPN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IFO4WS4Y","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IFO4WS4YJVODYMPNKSBQALL4YK","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-03-27T12:10:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3676a6904744c0f64f5b3aeef950acdea0f2cb9c8f464fe4cccb4e40b9f1d52b","abstract_canon_sha256":"92385a6b6f20ebdc273de493b26e4b7f11b6d861ffb11e271ddf96f364ee665e"},"schema_version":"1.0"},"canonical_sha256":"415dcb4b984d5c3c31ed5483002d7cc297305839ea6e7dffd6b7a30c91dd0468","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:39.678400Z","signature_b64":"mr53aXLaYtvcWsKMnqTqAG9IZ6uCkiIDBAm1gVpGj7bm47mOhisouOfj7WbIkDTIvwNcNos6ozbstVQfcRyoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"415dcb4b984d5c3c31ed5483002d7cc297305839ea6e7dffd6b7a30c91dd0468","last_reissued_at":"2026-05-18T03:29:39.677903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:39.677903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6799","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":"2026-05-18T03:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7xGYGJlN5iLU09vroR9zu1ubUJ1N5Vu7RaMbqN1xQCw02K7gh/+fbvBlVq1eQQV8dWNz7vYgirrCcp0uAwLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:58.065161Z"},"content_sha256":"47a4e5d9b465dd9e0d20ae2ababfeec65c14db9909d679be3032bb7d45565fca","schema_version":"1.0","event_id":"sha256:47a4e5d9b465dd9e0d20ae2ababfeec65c14db9909d679be3032bb7d45565fca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IFO4WS4YJVODYMPNKSBQALL4YK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proving the Pressing Game Conjecture on Linear Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Eliot Bixby, Istv\\'an Mikl\\'os, Toby Flint","submitted_at":"2013-03-27T12:10:15Z","abstract_excerpt":"The pressing game on black-and-white graphs is the following: Given a graph $G(V,E)$ with its vertices colored with black and white, any black vertex $v$ can be pressed, which has the following effect: (a) all neighbors of $v$ change color, i.e. white neighbors become black and \\emph{vice versa}, (b) all pairs of neighbors of $v$ change connectivity, i.e. connected pairs become unconnected, unconnected ones become connected, (c) and finally, $v$ becomes a separated white vertex. The aim of the game is to transform $G$ into an all white, empty graph. It is a known result that the all white empt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6799","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":"2026-05-18T03:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdBtRRfPRa+DYcX3p6ykpZ1AJipE2mQLmIUM30nParuA2FqqbFv3S2aavI268dnAejyu8qPaUasDvW76nGOxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:58.065526Z"},"content_sha256":"da443194fdaeeaa0b9d92598f49eb4728e90ae49522162da20226c88c1d0111f","schema_version":"1.0","event_id":"sha256:da443194fdaeeaa0b9d92598f49eb4728e90ae49522162da20226c88c1d0111f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IFO4WS4YJVODYMPNKSBQALL4YK/bundle.json","state_url":"https://pith.science/pith/IFO4WS4YJVODYMPNKSBQALL4YK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IFO4WS4YJVODYMPNKSBQALL4YK/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":"2026-06-23T16:18:58Z","links":{"resolver":"https://pith.science/pith/IFO4WS4YJVODYMPNKSBQALL4YK","bundle":"https://pith.science/pith/IFO4WS4YJVODYMPNKSBQALL4YK/bundle.json","state":"https://pith.science/pith/IFO4WS4YJVODYMPNKSBQALL4YK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IFO4WS4YJVODYMPNKSBQALL4YK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IFO4WS4YJVODYMPNKSBQALL4YK","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":"92385a6b6f20ebdc273de493b26e4b7f11b6d861ffb11e271ddf96f364ee665e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-03-27T12:10:15Z","title_canon_sha256":"3676a6904744c0f64f5b3aeef950acdea0f2cb9c8f464fe4cccb4e40b9f1d52b"},"schema_version":"1.0","source":{"id":"1303.6799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6799","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6799v1","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6799","created_at":"2026-05-18T03:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"IFO4WS4YJVOD","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IFO4WS4YJVODYMPN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IFO4WS4Y","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:da443194fdaeeaa0b9d92598f49eb4728e90ae49522162da20226c88c1d0111f","target":"graph","created_at":"2026-05-18T03:29:39Z","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 pressing game on black-and-white graphs is the following: Given a graph $G(V,E)$ with its vertices colored with black and white, any black vertex $v$ can be pressed, which has the following effect: (a) all neighbors of $v$ change color, i.e. white neighbors become black and \\emph{vice versa}, (b) all pairs of neighbors of $v$ change connectivity, i.e. connected pairs become unconnected, unconnected ones become connected, (c) and finally, $v$ becomes a separated white vertex. The aim of the game is to transform $G$ into an all white, empty graph. It is a known result that the all white empt","authors_text":"Eliot Bixby, Istv\\'an Mikl\\'os, Toby Flint","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-03-27T12:10:15Z","title":"Proving the Pressing Game Conjecture on Linear Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6799","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":"sha256:47a4e5d9b465dd9e0d20ae2ababfeec65c14db9909d679be3032bb7d45565fca","target":"record","created_at":"2026-05-18T03:29:39Z","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":"92385a6b6f20ebdc273de493b26e4b7f11b6d861ffb11e271ddf96f364ee665e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-03-27T12:10:15Z","title_canon_sha256":"3676a6904744c0f64f5b3aeef950acdea0f2cb9c8f464fe4cccb4e40b9f1d52b"},"schema_version":"1.0","source":{"id":"1303.6799","kind":"arxiv","version":1}},"canonical_sha256":"415dcb4b984d5c3c31ed5483002d7cc297305839ea6e7dffd6b7a30c91dd0468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"415dcb4b984d5c3c31ed5483002d7cc297305839ea6e7dffd6b7a30c91dd0468","first_computed_at":"2026-05-18T03:29:39.677903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:39.677903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mr53aXLaYtvcWsKMnqTqAG9IZ6uCkiIDBAm1gVpGj7bm47mOhisouOfj7WbIkDTIvwNcNos6ozbstVQfcRyoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:39.678400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a4e5d9b465dd9e0d20ae2ababfeec65c14db9909d679be3032bb7d45565fca","sha256:da443194fdaeeaa0b9d92598f49eb4728e90ae49522162da20226c88c1d0111f"],"state_sha256":"df9f8ece3a5d003a7d5269eb38979bc2d61b8d7290ae6f98fe24ff6e20a5abdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5xsu38nbOKqRU6NadTtHdI6wpCHX/Blcex1uiao5JeWOw2hzhOyw+e7rlKXOQ8ARP790frKYP1FM8agSzK+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:18:58.067442Z","bundle_sha256":"a25b838ef7e052f664d5228f1c8784dfbf60052c6bb90d5f2463298e1b016108"}}