{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TSVV6K2D4MWWPYYDOOAC56RV6I","short_pith_number":"pith:TSVV6K2D","canonical_record":{"source":{"id":"1105.1492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-08T06:07:55Z","cross_cats_sorted":[],"title_canon_sha256":"035b567041d9d00b83ededd80956b6b095081a7cb7aed231190a9ab336f6afd5","abstract_canon_sha256":"e57b91f8ececcf5e0af50a02d826e7704b7a0e453dc1835096e09217e20bed14"},"schema_version":"1.0"},"canonical_sha256":"9cab5f2b43e32d67e30373802efa35f220b9a8ff5a21d1986329ad46a6b1408c","source":{"kind":"arxiv","id":"1105.1492","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1492","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1492v1","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1492","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"TSVV6K2D4MWW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TSVV6K2D4MWWPYYD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TSVV6K2D","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TSVV6K2D4MWWPYYDOOAC56RV6I","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-08T06:07:55Z","cross_cats_sorted":[],"title_canon_sha256":"035b567041d9d00b83ededd80956b6b095081a7cb7aed231190a9ab336f6afd5","abstract_canon_sha256":"e57b91f8ececcf5e0af50a02d826e7704b7a0e453dc1835096e09217e20bed14"},"schema_version":"1.0"},"canonical_sha256":"9cab5f2b43e32d67e30373802efa35f220b9a8ff5a21d1986329ad46a6b1408c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:00.549861Z","signature_b64":"MAt+zRUdVX3mPrsvW97R8FzJIMLBMWRFzwnwtl5PLmPgsw3r4nOuTeAdq1jT/Ej+W16XgmOy94AzLDd6rFSmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cab5f2b43e32d67e30373802efa35f220b9a8ff5a21d1986329ad46a6b1408c","last_reissued_at":"2026-05-18T02:22:00.549175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:00.549175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1492","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":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVq2JdzaEM+uRH9Qkg3DNktnt6mdqmv7gAatSH3ol9mBloZ+8B9/K4uYNEWWOfNg+yVXxWHnSNskGqXruu/qDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:33.618177Z"},"content_sha256":"ba5b4ddee498dae7b8b960d0deca64b5fdc764e7edc76619eb95cd155a3a3f4b","schema_version":"1.0","event_id":"sha256:ba5b4ddee498dae7b8b960d0deca64b5fdc764e7edc76619eb95cd155a3a3f4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TSVV6K2D4MWWPYYDOOAC56RV6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iteration Index of a Zero Forcing Set in a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cong X. Kang, Eunjeong Yi, Kiran B. Chilakamarri, Nathaniel Dean","submitted_at":"2011-05-08T06:07:55Z","abstract_excerpt":"Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say, \"black\" and \"white\". Let Z denote the (initial) set of black vertices of G. The color-change rule converts the color of a vertex from white to black if the white vertex is the only white neighbor of a black vertex. The set Z is said to be a zero forcing set of G if all vertices of G will be turned black after finitely many applications of the color-change rule. The zero forcing number of G is the minimum of |Z| over all zero forcing sets Z \\subseteq V (G). Zero forcing parameters have been studied and applied to the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1492","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":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDBUQ33FJIr8rNtUHEGQfUqcPMkzmM1i1jvBgjr39hdqNqkYcPkJpzii6EdqxnQ75LcQxvvPE0YrrDMyV1ZyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:33.618774Z"},"content_sha256":"dffec5449f7e738590f112f853b4eaeb9c6d853130f4f8409d6db0d3b8c315ff","schema_version":"1.0","event_id":"sha256:dffec5449f7e738590f112f853b4eaeb9c6d853130f4f8409d6db0d3b8c315ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/bundle.json","state_url":"https://pith.science/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/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":"2026-06-06T20:09:33Z","links":{"resolver":"https://pith.science/pith/TSVV6K2D4MWWPYYDOOAC56RV6I","bundle":"https://pith.science/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/bundle.json","state":"https://pith.science/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSVV6K2D4MWWPYYDOOAC56RV6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TSVV6K2D4MWWPYYDOOAC56RV6I","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":"e57b91f8ececcf5e0af50a02d826e7704b7a0e453dc1835096e09217e20bed14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-08T06:07:55Z","title_canon_sha256":"035b567041d9d00b83ededd80956b6b095081a7cb7aed231190a9ab336f6afd5"},"schema_version":"1.0","source":{"id":"1105.1492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1492","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1492v1","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1492","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"TSVV6K2D4MWW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TSVV6K2D4MWWPYYD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TSVV6K2D","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:dffec5449f7e738590f112f853b4eaeb9c6d853130f4f8409d6db0d3b8c315ff","target":"graph","created_at":"2026-05-18T02:22:00Z","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":"Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say, \"black\" and \"white\". Let Z denote the (initial) set of black vertices of G. The color-change rule converts the color of a vertex from white to black if the white vertex is the only white neighbor of a black vertex. The set Z is said to be a zero forcing set of G if all vertices of G will be turned black after finitely many applications of the color-change rule. The zero forcing number of G is the minimum of |Z| over all zero forcing sets Z \\subseteq V (G). Zero forcing parameters have been studied and applied to the m","authors_text":"Cong X. Kang, Eunjeong Yi, Kiran B. Chilakamarri, Nathaniel Dean","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-08T06:07:55Z","title":"Iteration Index of a Zero Forcing Set in a Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1492","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:ba5b4ddee498dae7b8b960d0deca64b5fdc764e7edc76619eb95cd155a3a3f4b","target":"record","created_at":"2026-05-18T02:22:00Z","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":"e57b91f8ececcf5e0af50a02d826e7704b7a0e453dc1835096e09217e20bed14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-08T06:07:55Z","title_canon_sha256":"035b567041d9d00b83ededd80956b6b095081a7cb7aed231190a9ab336f6afd5"},"schema_version":"1.0","source":{"id":"1105.1492","kind":"arxiv","version":1}},"canonical_sha256":"9cab5f2b43e32d67e30373802efa35f220b9a8ff5a21d1986329ad46a6b1408c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cab5f2b43e32d67e30373802efa35f220b9a8ff5a21d1986329ad46a6b1408c","first_computed_at":"2026-05-18T02:22:00.549175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:00.549175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MAt+zRUdVX3mPrsvW97R8FzJIMLBMWRFzwnwtl5PLmPgsw3r4nOuTeAdq1jT/Ej+W16XgmOy94AzLDd6rFSmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:00.549861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba5b4ddee498dae7b8b960d0deca64b5fdc764e7edc76619eb95cd155a3a3f4b","sha256:dffec5449f7e738590f112f853b4eaeb9c6d853130f4f8409d6db0d3b8c315ff"],"state_sha256":"830ed58cc0750b69c32ab2482f10ac178f73687802c8ecb7664281fb2132b4d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKgdT0Ehl9GhLiu7IBobboQeURK7siFHbnWsnh4OOWzZF/di4cOQmGkwRQsAyR1g3vm4v2gIM3JhVhE4PuIDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:09:33.621888Z","bundle_sha256":"e287f7937a3d6ddb08acd43f8bed94a34c4b4da0689056b696a3bb2447ba05e6"}}