{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","short_pith_number":"pith:ZYWV7VMJ","canonical_record":{"source":{"id":"2607.07627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-08T16:43:19Z","cross_cats_sorted":["cs.CC","cs.GT"],"title_canon_sha256":"7561704e318a9070399545447fa1baf973ae9a1ebe3b4dec665850f9f44a5ae2","abstract_canon_sha256":"d69c8be4449c0a449dafddd14b2dabab31937c19de970c6aa77df1fd671d5a66"},"schema_version":"1.0"},"canonical_sha256":"ce2d5fd5896221b98b5777e053889dac55ac3dd79fa8d2c0db31e6fef8a90c21","source":{"kind":"arxiv","id":"2607.07627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07627","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07627v1","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07627","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZYWV7VMJMIQ3","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZYWV7VMJMIQ3TC2X","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZYWV7VMJ","created_at":"2026-07-09T01:20:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-08T16:43:19Z","cross_cats_sorted":["cs.CC","cs.GT"],"title_canon_sha256":"7561704e318a9070399545447fa1baf973ae9a1ebe3b4dec665850f9f44a5ae2","abstract_canon_sha256":"d69c8be4449c0a449dafddd14b2dabab31937c19de970c6aa77df1fd671d5a66"},"schema_version":"1.0"},"canonical_sha256":"ce2d5fd5896221b98b5777e053889dac55ac3dd79fa8d2c0db31e6fef8a90c21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:37.193980Z","signature_b64":"VhP6TfGh7nT1JUpGFAITkBXCpGpIE5nT/8qS8Kw22POIpP6bD30z134Ua2GW8BjSpkN2CIgEC2/a95+LrJyHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2d5fd5896221b98b5777e053889dac55ac3dd79fa8d2c0db31e6fef8a90c21","last_reissued_at":"2026-07-09T01:20:37.193550Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:37.193550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07627","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":"2026-07-09T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PgpzDxODPCNXssGEvOvR+Q1wVUx801fobRiHX5cU1GsyWAQBEY8vFLcuDYD9PKNCeXRSaUvRtr3nPffP1TVzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.414229Z"},"content_sha256":"7611b9e5b2199d0b2777399e8d22330797dfed902582df2102f461c7a407a075","schema_version":"1.0","event_id":"sha256:7611b9e5b2199d0b2777399e8d22330797dfed902582df2102f461c7a407a075"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pure Nash Equilibria in Graphical Games of Bounded Width Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.GT"],"primary_cat":"cs.DS","authors_text":"Michael Lampis, Yiren Lu","submitted_at":"2026-07-08T16:43:19Z","abstract_excerpt":"We revisit the complexity of deciding whether a graphical game admits a pure Nash equilibrium (PNE) parameterized by standard measures of the input graph, such as treewidth. The natural dynamic programming algorithm for this problem has parameter dependence $\\alpha^{(\\Delta+1)\\text{tw}}$ where $\\alpha$ is the maximum number of strategies available to each player, each player's utility depends on at most $\\Delta$ other players, and the input graph has width $\\text{tw}$. Our first contribution is to point out that an algorithm by Thomas and van Leeuwen [Algorithmica 2015] claiming to improve thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07627","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/2607.07627/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":"2026-07-09T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMp/hOeBXMUDHjQ+PENPSNuamiwKH2oi0ulJQvZTcAnI7EB2pd5ACd/Y2U6TWa7jt6g8xhdilM9wPEAy0vN5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.415018Z"},"content_sha256":"d0647f0db7ba1fe4fca04ab5b1a7ae992544b600f162a7ada9aee018b2f30044","schema_version":"1.0","event_id":"sha256:d0647f0db7ba1fe4fca04ab5b1a7ae992544b600f162a7ada9aee018b2f30044"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"integrity","payload":{"note":"URL 'https://dslpitt' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2607.07627","detector":"external_links","evidence":{"url":"https://dslpitt","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1783640354.0177457},"severity":"advisory","ref_index":null,"audited_at":"2026-07-09T23:39:14.019292Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://dslpitt","finding_type":"dead_url","evidence_hash":"f51287c602aab2e341eea0ac4622ab7091aefe2008a80970be4914ac25455763","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":11302,"payload_sha256":"18cd0932294b205a3d451da7cf32d90f0327618472c01d3325e47b4da1ffa08a","signature_b64":"2FpahEiJOMbmTGpxWg2IdG635vabG1ETsu50l1hJmciPdGT/z6aep1EToE3WL8PupA+trzjXMJ6B2zEJwd6bAw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T23:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X0aywA/ZvabqXN/N34lSArJ50iBYt/T3u5/ET4xIdj6H2+Uf2ii3Fh4J1uag42H7vokD/eqqW+FduBFbrVsZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.418120Z"},"content_sha256":"1317931a2893ef70b7cebb0af1a370473e0d361e143d6477af4115c99328202a","schema_version":"1.0","event_id":"sha256:1317931a2893ef70b7cebb0af1a370473e0d361e143d6477af4115c99328202a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"integrity","payload":{"note":"URL 'https://linkinghub' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2607.07627","detector":"external_links","evidence":{"url":"https://linkinghub","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1783640351.6988087},"severity":"advisory","ref_index":null,"audited_at":"2026-07-09T23:39:14.019292Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://linkinghub","finding_type":"dead_url","evidence_hash":"e45220341d327366fbbb079217c8eeb70dc0e6ca9aa9e365d8aca4d74281c571","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":11301,"payload_sha256":"7a7cf30fe5aed7983ac5d8db0adc87b47f04f6fd6611ea9a428c4a8cb10ae716","signature_b64":"yba/KbDaczyCEuVU/0pL3KIKhLiuqFpUikbK9aMjtotzY18xD1BEImatyaaBzlVWt9bAr01cftlDz2uY7KOECQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T23:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJ53rf8brF+cuH301+r1yQzhBPVg0vb0PTZnd5EGaG3zJlOwU+6j7IZtOVGiVlK0nNm9BGNw39QjFdRLnMc6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.418913Z"},"content_sha256":"2169741959f8e93029d9481cac8e8db2acc458c698002bb7e3c5b7f57f18a649","schema_version":"1.0","event_id":"sha256:2169741959f8e93029d9481cac8e8db2acc458c698002bb7e3c5b7f57f18a649"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"integrity","payload":{"note":"URL 'https://dslpitt' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2607.07627","detector":"external_links","evidence":{"url":"https://dslpitt","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1783597162.0034745},"severity":"advisory","ref_index":null,"audited_at":"2026-07-09T11:39:22.005011Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://dslpitt","finding_type":"dead_url","evidence_hash":"df1b5153712470b66b52d5be1085e461bdb9e5662f1c15a1761fe7d8c27a7b48","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":8703,"payload_sha256":"f86456347d2909de003d57c93454feffe50bd7548c74c84310904b7511e10a33","signature_b64":"eDTDSGHJp1nMTwV6aH3uvFXxd+0IP3CBkQOxJM+EedCPdF3L+hKUKG29hAMzvhBDI7JwA6scTjg0HjIW8V7XBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T11:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClZiTxFFO37hAKMnZ+0Ur4rS+Je0D3rYyEEFJnsYJTaLNY//j8RrD4l4rP10Vqhf2qiD9av5Gu2L/kq7EkxVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.419573Z"},"content_sha256":"5af50b6653f81b47a3067d2f54a2723f660534f3f9c142cf3e07321ff9245b25","schema_version":"1.0","event_id":"sha256:5af50b6653f81b47a3067d2f54a2723f660534f3f9c142cf3e07321ff9245b25"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","target":"integrity","payload":{"note":"URL 'https://linkinghub' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2607.07627","detector":"external_links","evidence":{"url":"https://linkinghub","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1783597159.8335404},"severity":"advisory","ref_index":null,"audited_at":"2026-07-09T11:39:22.005011Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://linkinghub","finding_type":"dead_url","evidence_hash":"9ddde8cbea22f33054a87ef80183b382ef2ae56a2b9563e23b3ee195db96d990","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":8702,"payload_sha256":"22679e773d9d33d3a7aa2e1bc8ababd9dce094512f501bbf1742bd1cd03592b9","signature_b64":"AkdlootLkx+2kM2E2SS0pJCbD7SFQFYow4u5ICJ5S1HzFeOvFD2LlISuxbF1INAsHPI4k2LDzZjzLtY/qVqOBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-09T11:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3oq3DeGDvMq9bKBO7nL+x/Tvh2GPfGSXw4JpwSTmR3PGbbYFvgr5/VL189POxCZACRNzXCAOeXKsMmeSS9ICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:37:18.420153Z"},"content_sha256":"0fff40e9c877a58739f0e79f841325ebb4e743f0d1e9d908ea7aa9dcc4a8c431","schema_version":"1.0","event_id":"sha256:0fff40e9c877a58739f0e79f841325ebb4e743f0d1e9d908ea7aa9dcc4a8c431"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/bundle.json","state_url":"https://pith.science/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/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":"2026-08-12T12:37:18Z","links":{"resolver":"https://pith.science/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR","bundle":"https://pith.science/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/bundle.json","state":"https://pith.science/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYWV7VMJMIQ3TC2XO7QFHCE5VR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZYWV7VMJMIQ3TC2XO7QFHCE5VR","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d69c8be4449c0a449dafddd14b2dabab31937c19de970c6aa77df1fd671d5a66","cross_cats_sorted":["cs.CC","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-08T16:43:19Z","title_canon_sha256":"7561704e318a9070399545447fa1baf973ae9a1ebe3b4dec665850f9f44a5ae2"},"schema_version":"1.0","source":{"id":"2607.07627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07627","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07627v1","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07627","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZYWV7VMJMIQ3","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZYWV7VMJMIQ3TC2X","created_at":"2026-07-09T01:20:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZYWV7VMJ","created_at":"2026-07-09T01:20:37Z"}],"graph_snapshots":[{"event_id":"sha256:d0647f0db7ba1fe4fca04ab5b1a7ae992544b600f162a7ada9aee018b2f30044","target":"graph","created_at":"2026-07-09T01:20:37Z","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/2607.07627/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the complexity of deciding whether a graphical game admits a pure Nash equilibrium (PNE) parameterized by standard measures of the input graph, such as treewidth. The natural dynamic programming algorithm for this problem has parameter dependence $\\alpha^{(\\Delta+1)\\text{tw}}$ where $\\alpha$ is the maximum number of strategies available to each player, each player's utility depends on at most $\\Delta$ other players, and the input graph has width $\\text{tw}$. Our first contribution is to point out that an algorithm by Thomas and van Leeuwen [Algorithmica 2015] claiming to improve thi","authors_text":"Michael Lampis, Yiren Lu","cross_cats":["cs.CC","cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-08T16:43:19Z","title":"Pure Nash Equilibria in Graphical Games of Bounded Width Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07627","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":"sha256:7611b9e5b2199d0b2777399e8d22330797dfed902582df2102f461c7a407a075","target":"record","created_at":"2026-07-09T01:20:37Z","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":"d69c8be4449c0a449dafddd14b2dabab31937c19de970c6aa77df1fd671d5a66","cross_cats_sorted":["cs.CC","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-08T16:43:19Z","title_canon_sha256":"7561704e318a9070399545447fa1baf973ae9a1ebe3b4dec665850f9f44a5ae2"},"schema_version":"1.0","source":{"id":"2607.07627","kind":"arxiv","version":1}},"canonical_sha256":"ce2d5fd5896221b98b5777e053889dac55ac3dd79fa8d2c0db31e6fef8a90c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce2d5fd5896221b98b5777e053889dac55ac3dd79fa8d2c0db31e6fef8a90c21","first_computed_at":"2026-07-09T01:20:37.193550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:37.193550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VhP6TfGh7nT1JUpGFAITkBXCpGpIE5nT/8qS8Kw22POIpP6bD30z134Ua2GW8BjSpkN2CIgEC2/a95+LrJyHAQ==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:37.193980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07627","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:0fff40e9c877a58739f0e79f841325ebb4e743f0d1e9d908ea7aa9dcc4a8c431","sha256:1317931a2893ef70b7cebb0af1a370473e0d361e143d6477af4115c99328202a","sha256:2169741959f8e93029d9481cac8e8db2acc458c698002bb7e3c5b7f57f18a649","sha256:5af50b6653f81b47a3067d2f54a2723f660534f3f9c142cf3e07321ff9245b25"]}],"invalid_events":[],"applied_event_ids":["sha256:7611b9e5b2199d0b2777399e8d22330797dfed902582df2102f461c7a407a075","sha256:d0647f0db7ba1fe4fca04ab5b1a7ae992544b600f162a7ada9aee018b2f30044"],"state_sha256":"b245f8c48d33cfecacbd35c70216482bf44c03ce5e48ee0e5549c6dcc238214e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+a7Cfqj7W8+Me8NfsJqND6RrnXDjDGzmxEYlF3gPXp+9DAhPKtpcebUxQEMD2vx+CUwxOMgW1BDPSI4eXKECAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T12:37:18.423520Z","bundle_sha256":"65a1dd51bb9c8c8c5a4af8036dcaeece4f149db47bc4720ebffb20ad26fe9859"}}