{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RHBU3UHC5PSWJOKCHENOFJOBAS","short_pith_number":"pith:RHBU3UHC","canonical_record":{"source":{"id":"1312.0964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T21:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"2cd1cdc241ed19172f83edb5a563c0fdaa089b2ea6a52131ee81aadfb8b5bb5b","abstract_canon_sha256":"85a5d2f079996939f983e1e96f55e01de0deeb5c98730dc532ce216009a7a7ee"},"schema_version":"1.0"},"canonical_sha256":"89c34dd0e2ebe564b942391ae2a5c104b3be0a12b749763a895c604f72f6a7d2","source":{"kind":"arxiv","id":"1312.0964","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0964","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0964v2","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0964","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"RHBU3UHC5PSW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHBU3UHC5PSWJOKC","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHBU3UHC","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RHBU3UHC5PSWJOKCHENOFJOBAS","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0964","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T21:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"2cd1cdc241ed19172f83edb5a563c0fdaa089b2ea6a52131ee81aadfb8b5bb5b","abstract_canon_sha256":"85a5d2f079996939f983e1e96f55e01de0deeb5c98730dc532ce216009a7a7ee"},"schema_version":"1.0"},"canonical_sha256":"89c34dd0e2ebe564b942391ae2a5c104b3be0a12b749763a895c604f72f6a7d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:33.162046Z","signature_b64":"Sd0PYQ4kDYsAemB6QbjJMwvPfenneqg1O9Bwgijnsnii6WR2Z2dzlk+0oHfmG4ogSAn4XTlxRJjoH3mr7AvtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89c34dd0e2ebe564b942391ae2a5c104b3be0a12b749763a895c604f72f6a7d2","last_reissued_at":"2026-05-18T03:01:33.161503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:33.161503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0964","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":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXBIPsiCxETM71nVh9VosAXa8y2nBjD0WgD+rFaQNWFiuXzQ82oYoZ3WGTcZ5MJidUmF/bXAIwB3Zow+/QTFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:27:25.215571Z"},"content_sha256":"58d5e85c0e224f4ccc3e40a599ae2d8799a25c44d86f8a28fefbb23e4113a63a","schema_version":"1.0","event_id":"sha256:58d5e85c0e224f4ccc3e40a599ae2d8799a25c44d86f8a28fefbb23e4113a63a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RHBU3UHC5PSWJOKCHENOFJOBAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The topology of competitively constructed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Wesley Pegden","submitted_at":"2013-12-03T21:40:59Z","abstract_excerpt":"We consider a simple game, the $k$-regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$. We show a sharp topological threshold for this game: for the case $k=3$ a player can ensure the resulting graph is planar, while for the case $k=4$, a player can force the appearance of arbitrarily large clique minors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0964","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":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmopDTV4POvmjRFcsZ5eqidUS9M0aPeKuu75T50iqSLjPLYwFsX7gMw0TmAnXCQLI1kCt/iilrkOMBni08+SAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:27:25.215922Z"},"content_sha256":"b99f096d1a7fcb792128810c9d4930532a4c83bf34e945c9dc5762957ce21acf","schema_version":"1.0","event_id":"sha256:b99f096d1a7fcb792128810c9d4930532a4c83bf34e945c9dc5762957ce21acf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/bundle.json","state_url":"https://pith.science/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/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":"2026-06-12T00:27:25Z","links":{"resolver":"https://pith.science/pith/RHBU3UHC5PSWJOKCHENOFJOBAS","bundle":"https://pith.science/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/bundle.json","state":"https://pith.science/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHBU3UHC5PSWJOKCHENOFJOBAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RHBU3UHC5PSWJOKCHENOFJOBAS","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":"85a5d2f079996939f983e1e96f55e01de0deeb5c98730dc532ce216009a7a7ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T21:40:59Z","title_canon_sha256":"2cd1cdc241ed19172f83edb5a563c0fdaa089b2ea6a52131ee81aadfb8b5bb5b"},"schema_version":"1.0","source":{"id":"1312.0964","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0964","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0964v2","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0964","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"RHBU3UHC5PSW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RHBU3UHC5PSWJOKC","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RHBU3UHC","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:b99f096d1a7fcb792128810c9d4930532a4c83bf34e945c9dc5762957ce21acf","target":"graph","created_at":"2026-05-18T03:01:33Z","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 consider a simple game, the $k$-regular graph game, in which players take turns adding edges to an initially empty graph subject to the constraint that the degrees of vertices cannot exceed $k$. We show a sharp topological threshold for this game: for the case $k=3$ a player can ensure the resulting graph is planar, while for the case $k=4$, a player can force the appearance of arbitrarily large clique minors.","authors_text":"Alan Frieze, Wesley Pegden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T21:40:59Z","title":"The topology of competitively constructed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0964","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":"sha256:58d5e85c0e224f4ccc3e40a599ae2d8799a25c44d86f8a28fefbb23e4113a63a","target":"record","created_at":"2026-05-18T03:01:33Z","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":"85a5d2f079996939f983e1e96f55e01de0deeb5c98730dc532ce216009a7a7ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-03T21:40:59Z","title_canon_sha256":"2cd1cdc241ed19172f83edb5a563c0fdaa089b2ea6a52131ee81aadfb8b5bb5b"},"schema_version":"1.0","source":{"id":"1312.0964","kind":"arxiv","version":2}},"canonical_sha256":"89c34dd0e2ebe564b942391ae2a5c104b3be0a12b749763a895c604f72f6a7d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89c34dd0e2ebe564b942391ae2a5c104b3be0a12b749763a895c604f72f6a7d2","first_computed_at":"2026-05-18T03:01:33.161503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:33.161503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sd0PYQ4kDYsAemB6QbjJMwvPfenneqg1O9Bwgijnsnii6WR2Z2dzlk+0oHfmG4ogSAn4XTlxRJjoH3mr7AvtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:33.162046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0964","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d5e85c0e224f4ccc3e40a599ae2d8799a25c44d86f8a28fefbb23e4113a63a","sha256:b99f096d1a7fcb792128810c9d4930532a4c83bf34e945c9dc5762957ce21acf"],"state_sha256":"9214efcc71341a55ddeda66965ab40b893574c31dc409f1a9546034173021475"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pFb8hk4haw+UOMVBd1kCTcjRGYwhSgvVAmKlnYDsp5NhKgZHKis7sJYGKxR/zMcRfJ9gnLi+pJAOtSsNB5GUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:27:25.217877Z","bundle_sha256":"e19bee4c0c7d41e7a524fe8060fb4fc6049fb0e7d586ced784e9cafcf9aca7dd"}}