{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BOKMJSELWBWJ5JDMFVXWOIBJKB","short_pith_number":"pith:BOKMJSEL","canonical_record":{"source":{"id":"2309.12265","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-21T17:17:00Z","cross_cats_sorted":["cs.DM","cs.GT"],"title_canon_sha256":"6ba0b101083034184e296e9ef6507c86a18dd6e0a8634176b2c9b3417c054984","abstract_canon_sha256":"71d891697cdea44d082d9e01f36ceb67a6f7db0fa1ab0758e3ad783f14f5d847"},"schema_version":"1.0"},"canonical_sha256":"0b94c4c88bb06c9ea46c2d6f672029507dd1e4bb0ffda5cda59f5e523cb88b5f","source":{"kind":"arxiv","id":"2309.12265","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12265","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12265v4","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12265","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"BOKMJSELWBWJ","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_16","alias_value":"BOKMJSELWBWJ5JDM","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_8","alias_value":"BOKMJSEL","created_at":"2026-07-05T09:30:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BOKMJSELWBWJ5JDMFVXWOIBJKB","target":"record","payload":{"canonical_record":{"source":{"id":"2309.12265","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-21T17:17:00Z","cross_cats_sorted":["cs.DM","cs.GT"],"title_canon_sha256":"6ba0b101083034184e296e9ef6507c86a18dd6e0a8634176b2c9b3417c054984","abstract_canon_sha256":"71d891697cdea44d082d9e01f36ceb67a6f7db0fa1ab0758e3ad783f14f5d847"},"schema_version":"1.0"},"canonical_sha256":"0b94c4c88bb06c9ea46c2d6f672029507dd1e4bb0ffda5cda59f5e523cb88b5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:56.862784Z","signature_b64":"sBZXmwV2yJYbQaXsYg12lG3HMFEToNMT3iu7+sDki1Mzcr/OwRNeu65Cne0oycAhCAOzSYn6sEFiKxNX0onCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b94c4c88bb06c9ea46c2d6f672029507dd1e4bb0ffda5cda59f5e523cb88b5f","last_reissued_at":"2026-07-05T09:30:56.862175Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:56.862175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.12265","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:30:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzwfrYI+20tq7W/bt7fAF69d7r4JPKey8g6Jbf96cguVmzc5LcfzMJkOzMKqM7A8eJuXPnmPCKunBZN+SSyxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:08:58.378205Z"},"content_sha256":"a785527124e30023c653e33d472225c7fa9dda409ab3a8511e1bfc5fac24a47f","schema_version":"1.0","event_id":"sha256:a785527124e30023c653e33d472225c7fa9dda409ab3a8511e1bfc5fac24a47f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BOKMJSELWBWJ5JDMFVXWOIBJKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cost-sharing in Parking Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.GT"],"primary_cat":"math.CO","authors_text":"Jan Kretschmann, J. Carlos Mart\\'inez Mori, Jennifer Elder, Pamela E. Harris","submitted_at":"2023-09-21T17:17:00Z","abstract_excerpt":"In this paper, we study the total displacement statistic of parking functions from the perspective of cooperative game theory. We introduce parking games, which are coalitional cost-sharing games in characteristic function form derived from the total displacement statistic. We show that parking games are supermodular cost-sharing games, indicating that cooperation is difficult (i.e., their core is empty). Next, we study their Shapley value, which formalizes a notion of \"fair\" cost-sharing and amounts to charging each car for its expected marginal displacement under a random arrival order. Our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12265","kind":"arxiv","version":4},"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/2309.12265/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":"2026-07-05T09:30:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vgIVyvytx9aLpaQo6JODVzRkKbYhOlXPC7sJL2+f8/oE2p7irtsvnJ7v55vW2g8dlU4V3yZ9oB6BeAnUDZGSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:08:58.378590Z"},"content_sha256":"bef51ef413582889d34f36a4443b51c0a277d7961e946dab47599e598815a0cc","schema_version":"1.0","event_id":"sha256:bef51ef413582889d34f36a4443b51c0a277d7961e946dab47599e598815a0cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/bundle.json","state_url":"https://pith.science/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/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":"2026-07-07T12:08:58Z","links":{"resolver":"https://pith.science/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB","bundle":"https://pith.science/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/bundle.json","state":"https://pith.science/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BOKMJSELWBWJ5JDMFVXWOIBJKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BOKMJSELWBWJ5JDMFVXWOIBJKB","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":"71d891697cdea44d082d9e01f36ceb67a6f7db0fa1ab0758e3ad783f14f5d847","cross_cats_sorted":["cs.DM","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-21T17:17:00Z","title_canon_sha256":"6ba0b101083034184e296e9ef6507c86a18dd6e0a8634176b2c9b3417c054984"},"schema_version":"1.0","source":{"id":"2309.12265","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12265","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12265v4","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12265","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_12","alias_value":"BOKMJSELWBWJ","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_16","alias_value":"BOKMJSELWBWJ5JDM","created_at":"2026-07-05T09:30:56Z"},{"alias_kind":"pith_short_8","alias_value":"BOKMJSEL","created_at":"2026-07-05T09:30:56Z"}],"graph_snapshots":[{"event_id":"sha256:bef51ef413582889d34f36a4443b51c0a277d7961e946dab47599e598815a0cc","target":"graph","created_at":"2026-07-05T09:30:56Z","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/2309.12265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the total displacement statistic of parking functions from the perspective of cooperative game theory. We introduce parking games, which are coalitional cost-sharing games in characteristic function form derived from the total displacement statistic. We show that parking games are supermodular cost-sharing games, indicating that cooperation is difficult (i.e., their core is empty). Next, we study their Shapley value, which formalizes a notion of \"fair\" cost-sharing and amounts to charging each car for its expected marginal displacement under a random arrival order. Our ","authors_text":"Jan Kretschmann, J. Carlos Mart\\'inez Mori, Jennifer Elder, Pamela E. Harris","cross_cats":["cs.DM","cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-21T17:17:00Z","title":"Cost-sharing in Parking Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12265","kind":"arxiv","version":4},"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:a785527124e30023c653e33d472225c7fa9dda409ab3a8511e1bfc5fac24a47f","target":"record","created_at":"2026-07-05T09:30:56Z","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":"71d891697cdea44d082d9e01f36ceb67a6f7db0fa1ab0758e3ad783f14f5d847","cross_cats_sorted":["cs.DM","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-09-21T17:17:00Z","title_canon_sha256":"6ba0b101083034184e296e9ef6507c86a18dd6e0a8634176b2c9b3417c054984"},"schema_version":"1.0","source":{"id":"2309.12265","kind":"arxiv","version":4}},"canonical_sha256":"0b94c4c88bb06c9ea46c2d6f672029507dd1e4bb0ffda5cda59f5e523cb88b5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b94c4c88bb06c9ea46c2d6f672029507dd1e4bb0ffda5cda59f5e523cb88b5f","first_computed_at":"2026-07-05T09:30:56.862175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:56.862175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sBZXmwV2yJYbQaXsYg12lG3HMFEToNMT3iu7+sDki1Mzcr/OwRNeu65Cne0oycAhCAOzSYn6sEFiKxNX0onCBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:56.862784Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.12265","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a785527124e30023c653e33d472225c7fa9dda409ab3a8511e1bfc5fac24a47f","sha256:bef51ef413582889d34f36a4443b51c0a277d7961e946dab47599e598815a0cc"],"state_sha256":"6fc6bf031abe79970ae73f9db959d141ca0cf7f2484cdbbfdc82599cdb9b2f82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RlyB+LjlR+Dgz8YiummDuCGbxFVeEg0G3EiNAiSF6qFzONYN40m6G4Hi2nKuZq6xJMS9AmN2VK7xKT84pNIyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:08:58.380588Z","bundle_sha256":"c64c6004820e45664176b69932aaeaa3b6d0a6bafac39ccb723d0cde877f483d"}}