{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZRH26FQBCHBNJV2WETLDVI25GK","short_pith_number":"pith:ZRH26FQB","canonical_record":{"source":{"id":"2504.14256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-04-19T10:20:40Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"7d6966aab45fd8b3f039908da503c717d6193417dcaacf8d4f99573c0740c239","abstract_canon_sha256":"49786a97a745b2a50c19fd31d0e7a66703cc7af8684b5f7349a1c7b0eeb4c773"},"schema_version":"1.0"},"canonical_sha256":"cc4faf160111c2d4d75624d63aa35d32a1eaa1116f0ea934621e92afc135c971","source":{"kind":"arxiv","id":"2504.14256","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14256","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14256v1","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14256","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZRH26FQBCHBN","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_16","alias_value":"ZRH26FQBCHBNJV2W","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_8","alias_value":"ZRH26FQB","created_at":"2026-07-05T10:51:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZRH26FQBCHBNJV2WETLDVI25GK","target":"record","payload":{"canonical_record":{"source":{"id":"2504.14256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-04-19T10:20:40Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"7d6966aab45fd8b3f039908da503c717d6193417dcaacf8d4f99573c0740c239","abstract_canon_sha256":"49786a97a745b2a50c19fd31d0e7a66703cc7af8684b5f7349a1c7b0eeb4c773"},"schema_version":"1.0"},"canonical_sha256":"cc4faf160111c2d4d75624d63aa35d32a1eaa1116f0ea934621e92afc135c971","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:40.718768Z","signature_b64":"eJiNUygG5d2KLtu7nyuwZTFkQXaHXldEKWk4qbiEFIPWEsC/81KMQGNCuilU623fNY/euG8YM2hXJ8S0AvDwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc4faf160111c2d4d75624d63aa35d32a1eaa1116f0ea934621e92afc135c971","last_reissued_at":"2026-07-05T10:51:40.718245Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:40.718245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.14256","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":"2026-07-05T10:51:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0OoZTWv5nNrb2sXuQPQJ/tTpkFs+r0PO+vkmp0IX5YF3/GeGTEfgwME/drYdts91D+TGZFVLVf/wzWncG+RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:19:55.347221Z"},"content_sha256":"8f6a8c70af7b6bfdd848c48b4c23cd87594f8764c5d5cc29b857a5d44fb49082","schema_version":"1.0","event_id":"sha256:8f6a8c70af7b6bfdd848c48b4c23cd87594f8764c5d5cc29b857a5d44fb49082"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZRH26FQBCHBNJV2WETLDVI25GK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maker-Maker games of rank 4 are PSPACE-complete","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DM","authors_text":"Florian Galliot, Jonas S\\'enizergues","submitted_at":"2025-04-19T10:20:40Z","abstract_excerpt":"The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge. Optimal play can only lead to a first player win or a draw, and deciding between the two is known to be PSPACE-complete even for 6-uniform hypergraphs. We establish PSPACE-completeness for hypergraphs of rank 4. As an intermediary, we use the recently introduced achievement positional games, a more general convention in which each player has their own winnin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14256","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.14256/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:51:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sw2/M69rrlpz24qkDYYmiE7JgGnvX1C7QxTZcAGea9UbCwECDvc2ytajfUva2qCm6qLKCXHsos6jWLNmHzEFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:19:55.347734Z"},"content_sha256":"a9034996c7e43416ba71cc9c3e78eddb17ecf54cf8877653bac07de748a7c683","schema_version":"1.0","event_id":"sha256:a9034996c7e43416ba71cc9c3e78eddb17ecf54cf8877653bac07de748a7c683"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRH26FQBCHBNJV2WETLDVI25GK/bundle.json","state_url":"https://pith.science/pith/ZRH26FQBCHBNJV2WETLDVI25GK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRH26FQBCHBNJV2WETLDVI25GK/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":"2026-08-24T02:19:55Z","links":{"resolver":"https://pith.science/pith/ZRH26FQBCHBNJV2WETLDVI25GK","bundle":"https://pith.science/pith/ZRH26FQBCHBNJV2WETLDVI25GK/bundle.json","state":"https://pith.science/pith/ZRH26FQBCHBNJV2WETLDVI25GK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRH26FQBCHBNJV2WETLDVI25GK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZRH26FQBCHBNJV2WETLDVI25GK","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":"49786a97a745b2a50c19fd31d0e7a66703cc7af8684b5f7349a1c7b0eeb4c773","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-04-19T10:20:40Z","title_canon_sha256":"7d6966aab45fd8b3f039908da503c717d6193417dcaacf8d4f99573c0740c239"},"schema_version":"1.0","source":{"id":"2504.14256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14256","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14256v1","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14256","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZRH26FQBCHBN","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_16","alias_value":"ZRH26FQBCHBNJV2W","created_at":"2026-07-05T10:51:40Z"},{"alias_kind":"pith_short_8","alias_value":"ZRH26FQB","created_at":"2026-07-05T10:51:40Z"}],"graph_snapshots":[{"event_id":"sha256:a9034996c7e43416ba71cc9c3e78eddb17ecf54cf8877653bac07de748a7c683","target":"graph","created_at":"2026-07-05T10:51:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.14256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge. Optimal play can only lead to a first player win or a draw, and deciding between the two is known to be PSPACE-complete even for 6-uniform hypergraphs. We establish PSPACE-completeness for hypergraphs of rank 4. As an intermediary, we use the recently introduced achievement positional games, a more general convention in which each player has their own winnin","authors_text":"Florian Galliot, Jonas S\\'enizergues","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-04-19T10:20:40Z","title":"Maker-Maker games of rank 4 are PSPACE-complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14256","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":"sha256:8f6a8c70af7b6bfdd848c48b4c23cd87594f8764c5d5cc29b857a5d44fb49082","target":"record","created_at":"2026-07-05T10:51:40Z","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":"49786a97a745b2a50c19fd31d0e7a66703cc7af8684b5f7349a1c7b0eeb4c773","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-04-19T10:20:40Z","title_canon_sha256":"7d6966aab45fd8b3f039908da503c717d6193417dcaacf8d4f99573c0740c239"},"schema_version":"1.0","source":{"id":"2504.14256","kind":"arxiv","version":1}},"canonical_sha256":"cc4faf160111c2d4d75624d63aa35d32a1eaa1116f0ea934621e92afc135c971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc4faf160111c2d4d75624d63aa35d32a1eaa1116f0ea934621e92afc135c971","first_computed_at":"2026-07-05T10:51:40.718245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:40.718245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eJiNUygG5d2KLtu7nyuwZTFkQXaHXldEKWk4qbiEFIPWEsC/81KMQGNCuilU623fNY/euG8YM2hXJ8S0AvDwCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:40.718768Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.14256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f6a8c70af7b6bfdd848c48b4c23cd87594f8764c5d5cc29b857a5d44fb49082","sha256:a9034996c7e43416ba71cc9c3e78eddb17ecf54cf8877653bac07de748a7c683"],"state_sha256":"fbc90f236d3fe6df0f2946d22bbe86796daf1703636daeaebbb2112dc53ae5f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSEwYgWtRYlhLBblQfRO8ETb8lUv/sRJfIygeynA4BCT4jjCOsIxzhh6uRyX6AHmWO/9p9wBFf1nNEfJhZSZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T02:19:55.351483Z","bundle_sha256":"c52131c7c73391ef93eb2ebc3876e77bae4dede534a06ba920cedace3b393a4c"}}