{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IEYKP7MSCCRZVFRIBSXVZ2XWAO","short_pith_number":"pith:IEYKP7MS","canonical_record":{"source":{"id":"1310.1281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-04T14:13:20Z","cross_cats_sorted":[],"title_canon_sha256":"03e003187c30a2a59b6373e3846e51e0b401f3df624e24f597b86dedeb1a96bd","abstract_canon_sha256":"9c789af8d8f8f55dd4508f56caed7aae6ad864de4abebe161cac3de1f266a8e0"},"schema_version":"1.0"},"canonical_sha256":"4130a7fd9210a39a96280caf5ceaf603bc20469a666f13e6717e40ba2024c414","source":{"kind":"arxiv","id":"1310.1281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1281","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1281v2","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1281","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"IEYKP7MSCCRZ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IEYKP7MSCCRZVFRI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IEYKP7MS","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IEYKP7MSCCRZVFRIBSXVZ2XWAO","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-04T14:13:20Z","cross_cats_sorted":[],"title_canon_sha256":"03e003187c30a2a59b6373e3846e51e0b401f3df624e24f597b86dedeb1a96bd","abstract_canon_sha256":"9c789af8d8f8f55dd4508f56caed7aae6ad864de4abebe161cac3de1f266a8e0"},"schema_version":"1.0"},"canonical_sha256":"4130a7fd9210a39a96280caf5ceaf603bc20469a666f13e6717e40ba2024c414","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.809115Z","signature_b64":"TVqFMfxTJimn9TKLKfjM+mzh/Bxu/WIkowmJti4kvWNV5oZAznb+UUkxkrzx9dwpA1VoFNzR7nFQHgLKZ7aLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4130a7fd9210a39a96280caf5ceaf603bc20469a666f13e6717e40ba2024c414","last_reissued_at":"2026-05-18T01:33:58.808586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.808586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1281","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":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oy6zENWnKRI1oXsdmNpbPdVHke1OjXk5334E8uWT03xAhIjDkzAxNpquZrpUEZJKsmI0U5tou+YCIqH7SBC5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:39:56.663455Z"},"content_sha256":"7df5fab9d6c4eba090b0d7eeaf2c645ffeda14b5c23558f0201d0d1b9d8eec34","schema_version":"1.0","event_id":"sha256:7df5fab9d6c4eba090b0d7eeaf2c645ffeda14b5c23558f0201d0d1b9d8eec34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IEYKP7MSCCRZVFRIBSXVZ2XWAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Games and Complexes I: Transformation via Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Richard J. Nowakowski, Sara Faridi, Svenja Huntemann","submitted_at":"2013-10-04T14:13:20Z","abstract_excerpt":"Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these simplicial complexes. These complexes are constructed using square-free monomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1281","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":"2026-05-18T01:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUon/b9LuisWcNS1uLGYctcRfOms5ClYTGPCCzMny/gdSbuHilFGx0m8qIo1lPt2K0WFIcw/YJuxGPF30NHoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:39:56.663792Z"},"content_sha256":"cf23e66338a2df2926bf99aa93e1501231e3d0025b0708edc088b4270b15288e","schema_version":"1.0","event_id":"sha256:cf23e66338a2df2926bf99aa93e1501231e3d0025b0708edc088b4270b15288e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/bundle.json","state_url":"https://pith.science/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/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":"2026-06-03T04:39:56Z","links":{"resolver":"https://pith.science/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO","bundle":"https://pith.science/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/bundle.json","state":"https://pith.science/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEYKP7MSCCRZVFRIBSXVZ2XWAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IEYKP7MSCCRZVFRIBSXVZ2XWAO","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":"9c789af8d8f8f55dd4508f56caed7aae6ad864de4abebe161cac3de1f266a8e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-04T14:13:20Z","title_canon_sha256":"03e003187c30a2a59b6373e3846e51e0b401f3df624e24f597b86dedeb1a96bd"},"schema_version":"1.0","source":{"id":"1310.1281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1281","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1281v2","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1281","created_at":"2026-05-18T01:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"IEYKP7MSCCRZ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IEYKP7MSCCRZVFRI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IEYKP7MS","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:cf23e66338a2df2926bf99aa93e1501231e3d0025b0708edc088b4270b15288e","target":"graph","created_at":"2026-05-18T01:33:58Z","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":"Placement games are a subclass of combinatorial games which are played on graphs. We will demonstrate that one can construct simplicial complexes corresponding to a placement game, and this game could be considered as a game played on these simplicial complexes. These complexes are constructed using square-free monomials.","authors_text":"Richard J. Nowakowski, Sara Faridi, Svenja Huntemann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-04T14:13:20Z","title":"Games and Complexes I: Transformation via Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1281","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":"sha256:7df5fab9d6c4eba090b0d7eeaf2c645ffeda14b5c23558f0201d0d1b9d8eec34","target":"record","created_at":"2026-05-18T01:33:58Z","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":"9c789af8d8f8f55dd4508f56caed7aae6ad864de4abebe161cac3de1f266a8e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-04T14:13:20Z","title_canon_sha256":"03e003187c30a2a59b6373e3846e51e0b401f3df624e24f597b86dedeb1a96bd"},"schema_version":"1.0","source":{"id":"1310.1281","kind":"arxiv","version":2}},"canonical_sha256":"4130a7fd9210a39a96280caf5ceaf603bc20469a666f13e6717e40ba2024c414","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4130a7fd9210a39a96280caf5ceaf603bc20469a666f13e6717e40ba2024c414","first_computed_at":"2026-05-18T01:33:58.808586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:58.808586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TVqFMfxTJimn9TKLKfjM+mzh/Bxu/WIkowmJti4kvWNV5oZAznb+UUkxkrzx9dwpA1VoFNzR7nFQHgLKZ7aLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:58.809115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7df5fab9d6c4eba090b0d7eeaf2c645ffeda14b5c23558f0201d0d1b9d8eec34","sha256:cf23e66338a2df2926bf99aa93e1501231e3d0025b0708edc088b4270b15288e"],"state_sha256":"682f861328ea1e65f68f6cea062f8980fba581c34ef5ae53e49ba9444056f21f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSFYolBiTqgsJyeOEvNvnZuw+NO6cqwwLJ7ezefydCE7jMVtxyKaKrUpP9PUe/I40EtG7BLWXUmXBTcoDa3MCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:39:56.665724Z","bundle_sha256":"31c0580ae29d0732136ddfa0e999fe9e6aaca7bd14cb4a3db95c6a8735be0108"}}