{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:6HUFFXKWBIPCR7J2JIBVKDKNX2","short_pith_number":"pith:6HUFFXKW","canonical_record":{"source":{"id":"0806.4956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-06-30T17:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"4a1db79b810b50d54521d239377f2ec22469668fde1fc363cda070922e9396f3","abstract_canon_sha256":"7b4f2466cc5079307dc3f1fc18a731c57c9c9dbcfc92516326a0747c7203d118"},"schema_version":"1.0"},"canonical_sha256":"f1e852dd560a1e28fd3a4a03550d4dbea9dbbe148551a1801eb4f1e2bc48af49","source":{"kind":"arxiv","id":"0806.4956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4956","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4956v2","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4956","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"6HUFFXKWBIPC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6HUFFXKWBIPCR7J2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6HUFFXKW","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:6HUFFXKWBIPCR7J2JIBVKDKNX2","target":"record","payload":{"canonical_record":{"source":{"id":"0806.4956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-06-30T17:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"4a1db79b810b50d54521d239377f2ec22469668fde1fc363cda070922e9396f3","abstract_canon_sha256":"7b4f2466cc5079307dc3f1fc18a731c57c9c9dbcfc92516326a0747c7203d118"},"schema_version":"1.0"},"canonical_sha256":"f1e852dd560a1e28fd3a4a03550d4dbea9dbbe148551a1801eb4f1e2bc48af49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:42.390460Z","signature_b64":"oQPo5uJjKA+AySqohzUn/Aao0ztXLKke1J0zYfkHRvHaELbBiUv4/MJoOYtv7bjdxd739uEHSJcQLcUkEiWqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e852dd560a1e28fd3a4a03550d4dbea9dbbe148551a1801eb4f1e2bc48af49","last_reissued_at":"2026-05-18T01:37:42.389766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:42.389766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.4956","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":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4L6oYPPiVrcIA/WZ8oWDzsveirIw+xSEZ/BHsOTKDTwXxq5vJbFevENv8ngfnn2uvPPpKT2TtkNFPv/2IxXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:36:08.661392Z"},"content_sha256":"943ead16141d28a8f1a3edf33d6ab891bdeb44b24cba6416780e42e98865cb66","schema_version":"1.0","event_id":"sha256:943ead16141d28a8f1a3edf33d6ab891bdeb44b24cba6416780e42e98865cb66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:6HUFFXKWBIPCR7J2JIBVKDKNX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Game Refinement Relations and Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Luca de Alfaro, Mari\\\"elle Stoelinga, Rupak Majumdar, Vishwanath Raman","submitted_at":"2008-06-30T17:55:15Z","abstract_excerpt":"We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state?\n  On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4956","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":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGadFxk7B5pv1ylIhRCIszuSEPhc/+QPYyxP44a5eWu7DCR/D5wf8/ZOr9chARtmB/MOSKLtEJH2Gn4myO/qAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:36:08.662026Z"},"content_sha256":"23d3c98d7c7b8edf3347609028d5917fa6a1d3cda808235b9606d7cf61487a02","schema_version":"1.0","event_id":"sha256:23d3c98d7c7b8edf3347609028d5917fa6a1d3cda808235b9606d7cf61487a02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/bundle.json","state_url":"https://pith.science/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/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":"2026-06-08T01:36:08Z","links":{"resolver":"https://pith.science/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2","bundle":"https://pith.science/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/bundle.json","state":"https://pith.science/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HUFFXKWBIPCR7J2JIBVKDKNX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6HUFFXKWBIPCR7J2JIBVKDKNX2","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":"7b4f2466cc5079307dc3f1fc18a731c57c9c9dbcfc92516326a0747c7203d118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-06-30T17:55:15Z","title_canon_sha256":"4a1db79b810b50d54521d239377f2ec22469668fde1fc363cda070922e9396f3"},"schema_version":"1.0","source":{"id":"0806.4956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4956","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4956v2","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4956","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"6HUFFXKWBIPC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6HUFFXKWBIPCR7J2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6HUFFXKW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:23d3c98d7c7b8edf3347609028d5917fa6a1d3cda808235b9606d7cf61487a02","target":"graph","created_at":"2026-05-18T01:37:42Z","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 two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal, for example, reach a target state, the question of winning is thus a probabilistic one: what is the maximal probability of winning from a given state?\n  On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two stat","authors_text":"Luca de Alfaro, Mari\\\"elle Stoelinga, Rupak Majumdar, Vishwanath Raman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-06-30T17:55:15Z","title":"Game Refinement Relations and Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4956","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":"sha256:943ead16141d28a8f1a3edf33d6ab891bdeb44b24cba6416780e42e98865cb66","target":"record","created_at":"2026-05-18T01:37:42Z","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":"7b4f2466cc5079307dc3f1fc18a731c57c9c9dbcfc92516326a0747c7203d118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-06-30T17:55:15Z","title_canon_sha256":"4a1db79b810b50d54521d239377f2ec22469668fde1fc363cda070922e9396f3"},"schema_version":"1.0","source":{"id":"0806.4956","kind":"arxiv","version":2}},"canonical_sha256":"f1e852dd560a1e28fd3a4a03550d4dbea9dbbe148551a1801eb4f1e2bc48af49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e852dd560a1e28fd3a4a03550d4dbea9dbbe148551a1801eb4f1e2bc48af49","first_computed_at":"2026-05-18T01:37:42.389766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:42.389766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oQPo5uJjKA+AySqohzUn/Aao0ztXLKke1J0zYfkHRvHaELbBiUv4/MJoOYtv7bjdxd739uEHSJcQLcUkEiWqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:42.390460Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:943ead16141d28a8f1a3edf33d6ab891bdeb44b24cba6416780e42e98865cb66","sha256:23d3c98d7c7b8edf3347609028d5917fa6a1d3cda808235b9606d7cf61487a02"],"state_sha256":"e28428069a2070fc7024b95d65a4e1039cbe79817ec99133a996f7205ded1507"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QshmlqDKwe/LZRal5tzqfMt6HK/frOQ5IgV8K3jcW0oqe0Ar6Pl0frfMlHjwfst3r/KI0nF57k8K4dPrkBvDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:36:08.665461Z","bundle_sha256":"c6e7c4c9e3d861b2e896c1e5233f52e9a05fb2d1aaada55807c98ec5dbe787e9"}}