{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7TDCMGURC2DO2IP4XTN75QSMY4","short_pith_number":"pith:7TDCMGUR","canonical_record":{"source":{"id":"1007.1371","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-08T13:29:35Z","cross_cats_sorted":["cs.DM","cs.GT","math.CO","math.PR"],"title_canon_sha256":"6d7ebf0adc85d3b7ed059da6e53b68d94222e6166ebbf6f0b033af8919dc06fc","abstract_canon_sha256":"364bd6c46d731090f98b23ad099d823a4dbc08b99c642909c8db616ad9b1099f"},"schema_version":"1.0"},"canonical_sha256":"fcc6261a911686ed21fcbcdbfec24cc72dc18d3c342bfcd2b7711b63e24627ec","source":{"kind":"arxiv","id":"1007.1371","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1371","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1371v3","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1371","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"7TDCMGURC2DO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7TDCMGURC2DO2IP4","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7TDCMGUR","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7TDCMGURC2DO2IP4XTN75QSMY4","target":"record","payload":{"canonical_record":{"source":{"id":"1007.1371","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-08T13:29:35Z","cross_cats_sorted":["cs.DM","cs.GT","math.CO","math.PR"],"title_canon_sha256":"6d7ebf0adc85d3b7ed059da6e53b68d94222e6166ebbf6f0b033af8919dc06fc","abstract_canon_sha256":"364bd6c46d731090f98b23ad099d823a4dbc08b99c642909c8db616ad9b1099f"},"schema_version":"1.0"},"canonical_sha256":"fcc6261a911686ed21fcbcdbfec24cc72dc18d3c342bfcd2b7711b63e24627ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:38.415268Z","signature_b64":"TcbHi7pv1LA3C/isxfjUPV7AKoJrV1slfOsd/q3hXGi4K/KMFQfI2QbK9HsCHVm8BV+4BDh2z6gPwJXwAGV3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcc6261a911686ed21fcbcdbfec24cc72dc18d3c342bfcd2b7711b63e24627ec","last_reissued_at":"2026-05-18T03:58:38.414787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:38.414787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.1371","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIAVAhsuMZz8iyCp6uKdRaIkbBh+FScEQ6PP0sGzKKOzHKorPFhxQ38mjYqjbvRdkog03Q7EAd17p+GM3absAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:22:34.413262Z"},"content_sha256":"399f727be68e8eebeb37b0c0fd05e6f585ddf65b0548fcaf6fff8bc86a335aa8","schema_version":"1.0","event_id":"sha256:399f727be68e8eebeb37b0c0fd05e6f585ddf65b0548fcaf6fff8bc86a335aa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7TDCMGURC2DO2IP4XTN75QSMY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finiteness in the Card Game of War","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.GT","math.CO","math.PR"],"primary_cat":"math.DS","authors_text":"Evgeny Lakshtanov, Vera Roshchina","submitted_at":"2010-07-08T13:29:35Z","abstract_excerpt":"The game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card collects both and returns them to the bottom of his hand. The player left with no cards loses. Those who played this game in their childhood did not always have enough patience to wait until the end of the game. A player who has collected almost all the cards can lose all but a few cards in the next 3 minutes. That way the children essentially conduct mathematical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1371","kind":"arxiv","version":3},"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":"2026-05-18T03:58:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLmprM0diklo7uUBe0RMkbGVyRD+YeAzQYZfNSbs+hgsKxkVySiMTd5Fo0/KUELLX5yPouviOLKQ5mvC/FOfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:22:34.413631Z"},"content_sha256":"0c2426b7ba54b7eb80a6adb02fff9381f4281557b27fdbdd4be9a7ef87bd96dd","schema_version":"1.0","event_id":"sha256:0c2426b7ba54b7eb80a6adb02fff9381f4281557b27fdbdd4be9a7ef87bd96dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TDCMGURC2DO2IP4XTN75QSMY4/bundle.json","state_url":"https://pith.science/pith/7TDCMGURC2DO2IP4XTN75QSMY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TDCMGURC2DO2IP4XTN75QSMY4/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":"2026-06-01T06:22:34Z","links":{"resolver":"https://pith.science/pith/7TDCMGURC2DO2IP4XTN75QSMY4","bundle":"https://pith.science/pith/7TDCMGURC2DO2IP4XTN75QSMY4/bundle.json","state":"https://pith.science/pith/7TDCMGURC2DO2IP4XTN75QSMY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TDCMGURC2DO2IP4XTN75QSMY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7TDCMGURC2DO2IP4XTN75QSMY4","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":"364bd6c46d731090f98b23ad099d823a4dbc08b99c642909c8db616ad9b1099f","cross_cats_sorted":["cs.DM","cs.GT","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-08T13:29:35Z","title_canon_sha256":"6d7ebf0adc85d3b7ed059da6e53b68d94222e6166ebbf6f0b033af8919dc06fc"},"schema_version":"1.0","source":{"id":"1007.1371","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1371","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1371v3","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1371","created_at":"2026-05-18T03:58:38Z"},{"alias_kind":"pith_short_12","alias_value":"7TDCMGURC2DO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7TDCMGURC2DO2IP4","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7TDCMGUR","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:0c2426b7ba54b7eb80a6adb02fff9381f4281557b27fdbdd4be9a7ef87bd96dd","target":"graph","created_at":"2026-05-18T03:58:38Z","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 game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card collects both and returns them to the bottom of his hand. The player left with no cards loses. Those who played this game in their childhood did not always have enough patience to wait until the end of the game. A player who has collected almost all the cards can lose all but a few cards in the next 3 minutes. That way the children essentially conduct mathematical ","authors_text":"Evgeny Lakshtanov, Vera Roshchina","cross_cats":["cs.DM","cs.GT","math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-08T13:29:35Z","title":"Finiteness in the Card Game of War"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1371","kind":"arxiv","version":3},"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":"sha256:399f727be68e8eebeb37b0c0fd05e6f585ddf65b0548fcaf6fff8bc86a335aa8","target":"record","created_at":"2026-05-18T03:58:38Z","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":"364bd6c46d731090f98b23ad099d823a4dbc08b99c642909c8db616ad9b1099f","cross_cats_sorted":["cs.DM","cs.GT","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-08T13:29:35Z","title_canon_sha256":"6d7ebf0adc85d3b7ed059da6e53b68d94222e6166ebbf6f0b033af8919dc06fc"},"schema_version":"1.0","source":{"id":"1007.1371","kind":"arxiv","version":3}},"canonical_sha256":"fcc6261a911686ed21fcbcdbfec24cc72dc18d3c342bfcd2b7711b63e24627ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcc6261a911686ed21fcbcdbfec24cc72dc18d3c342bfcd2b7711b63e24627ec","first_computed_at":"2026-05-18T03:58:38.414787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:38.414787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TcbHi7pv1LA3C/isxfjUPV7AKoJrV1slfOsd/q3hXGi4K/KMFQfI2QbK9HsCHVm8BV+4BDh2z6gPwJXwAGV3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:38.415268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1371","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:399f727be68e8eebeb37b0c0fd05e6f585ddf65b0548fcaf6fff8bc86a335aa8","sha256:0c2426b7ba54b7eb80a6adb02fff9381f4281557b27fdbdd4be9a7ef87bd96dd"],"state_sha256":"75c0fae5991bc8b719cb7e0d2a33429983d8125da97c34d24a8f0e774f5c35dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"almRgOi0iAAa5x5aQXGqE/9WdRirxlaYW77rxnTv/RTH0KD6DjsYeiS4VJD2A1xI5K8fqRP4pU5OogjMeev8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:22:34.415665Z","bundle_sha256":"270f9a7d5deeaaf35b614062a3bd7e7d3555308b8a1d3b1da8f409f930dc47a3"}}