{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3JERFDITWBX4PYQGTA4S33QEF6","short_pith_number":"pith:3JERFDIT","canonical_record":{"source":{"id":"1411.5751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-21T03:06:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"385cd90199433cb9166d43deaefb7dfc4cf45890f1ea4d938a54286c9cac9c35","abstract_canon_sha256":"647cc9346cf3d7fba81bb400b74e8673251b53ceba93ff88a1916086d725f34d"},"schema_version":"1.0"},"canonical_sha256":"da49128d13b06fc7e20698392dee042f84d075c1453f8d41d3032ff91661c21b","source":{"kind":"arxiv","id":"1411.5751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5751","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5751v1","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5751","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"3JERFDITWBX4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3JERFDITWBX4PYQG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3JERFDIT","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3JERFDITWBX4PYQGTA4S33QEF6","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-21T03:06:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"385cd90199433cb9166d43deaefb7dfc4cf45890f1ea4d938a54286c9cac9c35","abstract_canon_sha256":"647cc9346cf3d7fba81bb400b74e8673251b53ceba93ff88a1916086d725f34d"},"schema_version":"1.0"},"canonical_sha256":"da49128d13b06fc7e20698392dee042f84d075c1453f8d41d3032ff91661c21b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:07.170914Z","signature_b64":"0/CwJx3CBkEamXn7CSSRFZUilrTo2fuuVbuOdi24PFVAhJOv3ZnzCLgTzDZeq8wLloHe4dTYDaP6ogSI13YrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da49128d13b06fc7e20698392dee042f84d075c1453f8d41d3032ff91661c21b","last_reissued_at":"2026-05-18T02:33:07.170376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:07.170376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5751","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":"2026-05-18T02:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WUsfGCutF7jRHZkq6ai38XNrlJVsxTRvs66claf1i5Ou79CSiTZ5cqt4/tvftrNCNxCXEjcVCt7BGOOF2lmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:37:10.177736Z"},"content_sha256":"c642ab3f6b47b4612f5385e28f21474426bcd4eee2463b8470a056b4b71c7821","schema_version":"1.0","event_id":"sha256:c642ab3f6b47b4612f5385e28f21474426bcd4eee2463b8470a056b4b71c7821"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3JERFDITWBX4PYQGTA4S33QEF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a memory game and preferential attachment graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Huseyin Acan, Pawel Hitczenko","submitted_at":"2014-11-21T03:06:23Z","abstract_excerpt":"In a recent paper Velleman and Warrington analyzed the expected values of some of the parameters in a memory game, namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively.\n  We also make a connection between the memory game and one of the models of preferential attachment"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5751","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":"2026-05-18T02:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4EAmUSiQXGYG3kKCJmzLen5Q0W+oVsWlzK6jLqC9g4FsGbrTMPRjyPnGmF1eHYq53larATM+tV+7OpVhZRvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:37:10.178087Z"},"content_sha256":"0d964e2d319793441ac370af8f44835070513aefea120134a2a185926943702f","schema_version":"1.0","event_id":"sha256:0d964e2d319793441ac370af8f44835070513aefea120134a2a185926943702f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JERFDITWBX4PYQGTA4S33QEF6/bundle.json","state_url":"https://pith.science/pith/3JERFDITWBX4PYQGTA4S33QEF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JERFDITWBX4PYQGTA4S33QEF6/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":"2026-06-03T01:37:10Z","links":{"resolver":"https://pith.science/pith/3JERFDITWBX4PYQGTA4S33QEF6","bundle":"https://pith.science/pith/3JERFDITWBX4PYQGTA4S33QEF6/bundle.json","state":"https://pith.science/pith/3JERFDITWBX4PYQGTA4S33QEF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JERFDITWBX4PYQGTA4S33QEF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3JERFDITWBX4PYQGTA4S33QEF6","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":"647cc9346cf3d7fba81bb400b74e8673251b53ceba93ff88a1916086d725f34d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-21T03:06:23Z","title_canon_sha256":"385cd90199433cb9166d43deaefb7dfc4cf45890f1ea4d938a54286c9cac9c35"},"schema_version":"1.0","source":{"id":"1411.5751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5751","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5751v1","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5751","created_at":"2026-05-18T02:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"3JERFDITWBX4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3JERFDITWBX4PYQG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3JERFDIT","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:0d964e2d319793441ac370af8f44835070513aefea120134a2a185926943702f","target":"graph","created_at":"2026-05-18T02:33:07Z","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":"In a recent paper Velleman and Warrington analyzed the expected values of some of the parameters in a memory game, namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively.\n  We also make a connection between the memory game and one of the models of preferential attachment","authors_text":"Huseyin Acan, Pawel Hitczenko","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-21T03:06:23Z","title":"On a memory game and preferential attachment graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5751","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:c642ab3f6b47b4612f5385e28f21474426bcd4eee2463b8470a056b4b71c7821","target":"record","created_at":"2026-05-18T02:33:07Z","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":"647cc9346cf3d7fba81bb400b74e8673251b53ceba93ff88a1916086d725f34d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-21T03:06:23Z","title_canon_sha256":"385cd90199433cb9166d43deaefb7dfc4cf45890f1ea4d938a54286c9cac9c35"},"schema_version":"1.0","source":{"id":"1411.5751","kind":"arxiv","version":1}},"canonical_sha256":"da49128d13b06fc7e20698392dee042f84d075c1453f8d41d3032ff91661c21b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da49128d13b06fc7e20698392dee042f84d075c1453f8d41d3032ff91661c21b","first_computed_at":"2026-05-18T02:33:07.170376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:07.170376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/CwJx3CBkEamXn7CSSRFZUilrTo2fuuVbuOdi24PFVAhJOv3ZnzCLgTzDZeq8wLloHe4dTYDaP6ogSI13YrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:07.170914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c642ab3f6b47b4612f5385e28f21474426bcd4eee2463b8470a056b4b71c7821","sha256:0d964e2d319793441ac370af8f44835070513aefea120134a2a185926943702f"],"state_sha256":"6fb0466326446977b9e4b10bebdb52f8d7cef5017c785e80c9b24757244aec61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItiDhefO1tEbK3BdZO3ixQa6kXvpc66+L5mOi5YN3YpM827dLjJWvxyWtQxTOajSsGLjCoLuGTN3QL7/PnMlBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:37:10.180073Z","bundle_sha256":"d29f755fcd63d731dd4879aedace9dbfa6b29753ac0896b1c73cbea35eb4f737"}}