{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CHEPBXEXLU6PAWUMEDNC4VCDF4","short_pith_number":"pith:CHEPBXEX","canonical_record":{"source":{"id":"1306.0294","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-03T04:38:01Z","cross_cats_sorted":[],"title_canon_sha256":"858ef4f9caa53a0adc55c965880e09bf87342fea7bdaa81dfe0d9fdff22eb304","abstract_canon_sha256":"e177a91286947f19707d1b3eed61b74aa9df7a708c03992ba99518055b33bcbc"},"schema_version":"1.0"},"canonical_sha256":"11c8f0dc975d3cf05a8c20da2e54432f36ba039ed8356a200746781e788b915f","source":{"kind":"arxiv","id":"1306.0294","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0294","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0294v5","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0294","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"CHEPBXEXLU6P","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CHEPBXEXLU6PAWUM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CHEPBXEX","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CHEPBXEXLU6PAWUMEDNC4VCDF4","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0294","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-03T04:38:01Z","cross_cats_sorted":[],"title_canon_sha256":"858ef4f9caa53a0adc55c965880e09bf87342fea7bdaa81dfe0d9fdff22eb304","abstract_canon_sha256":"e177a91286947f19707d1b3eed61b74aa9df7a708c03992ba99518055b33bcbc"},"schema_version":"1.0"},"canonical_sha256":"11c8f0dc975d3cf05a8c20da2e54432f36ba039ed8356a200746781e788b915f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:22.035968Z","signature_b64":"9aJYNWrt/pWNJJgJpwolmqhpMIfq2/b1WlR9qr7wLE2+JzGN51Zjm3/b+PZUb9EkrfTYBQ/MPZzWlVA3+tE2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11c8f0dc975d3cf05a8c20da2e54432f36ba039ed8356a200746781e788b915f","last_reissued_at":"2026-05-18T03:12:22.035030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:22.035030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0294","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJuH/U2JOqmq+B5YMjV6PZXuJybPxrFeJ5hugjqGAmT6oXklsBSuLddY+szX3JSHRZ17+DGl4j6rcKTx5VkOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T14:04:46.675548Z"},"content_sha256":"6e56b442e19b636f761b89784d1d946601f776dcb357178f22f47ba91087814c","schema_version":"1.0","event_id":"sha256:6e56b442e19b636f761b89784d1d946601f776dcb357178f22f47ba91087814c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CHEPBXEXLU6PAWUMEDNC4VCDF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chip-firing game and partial Tutte polynomial for Eulerian digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"K\\'evin Perrot, Trung Van Pham","submitted_at":"2013-06-03T04:38:01Z","abstract_excerpt":"The Chip-firing game is a discrete dynamical system played on a graph, in which chips move along edges according to a simple local rule. Properties of the underlying graph are of course useful to the understanding of the game, but since a conjecture of Biggs that was proved by Merino L\\'opez, we also know that the study of the Chip-firing game can give insights on the graph. In particular, a strong relation between the partial Tutte polynomial $T_G(1,y)$ and the set of recurrent configurations of a Chip-firing game (with a distinguished sink vertex) has been established for undirected graphs. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0294","kind":"arxiv","version":5},"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":"2026-05-18T03:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y30yQz5POZrAWmJiTmKkZ6p0/wtd7AiCXH93/7N9subFURgGP/eIX312Dp2vMhUow4yakDEEEXhh/0k43+fJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T14:04:46.676230Z"},"content_sha256":"22ffdd851d6db276741d57ce71c9c6da7a21ea1ce4cedd0d83b67a05e2a10a69","schema_version":"1.0","event_id":"sha256:22ffdd851d6db276741d57ce71c9c6da7a21ea1ce4cedd0d83b67a05e2a10a69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/bundle.json","state_url":"https://pith.science/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/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":"2026-05-20T14:04:46Z","links":{"resolver":"https://pith.science/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4","bundle":"https://pith.science/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/bundle.json","state":"https://pith.science/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHEPBXEXLU6PAWUMEDNC4VCDF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CHEPBXEXLU6PAWUMEDNC4VCDF4","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":"e177a91286947f19707d1b3eed61b74aa9df7a708c03992ba99518055b33bcbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-03T04:38:01Z","title_canon_sha256":"858ef4f9caa53a0adc55c965880e09bf87342fea7bdaa81dfe0d9fdff22eb304"},"schema_version":"1.0","source":{"id":"1306.0294","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0294","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0294v5","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0294","created_at":"2026-05-18T03:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"CHEPBXEXLU6P","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CHEPBXEXLU6PAWUM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CHEPBXEX","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:22ffdd851d6db276741d57ce71c9c6da7a21ea1ce4cedd0d83b67a05e2a10a69","target":"graph","created_at":"2026-05-18T03:12:22Z","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 Chip-firing game is a discrete dynamical system played on a graph, in which chips move along edges according to a simple local rule. Properties of the underlying graph are of course useful to the understanding of the game, but since a conjecture of Biggs that was proved by Merino L\\'opez, we also know that the study of the Chip-firing game can give insights on the graph. In particular, a strong relation between the partial Tutte polynomial $T_G(1,y)$ and the set of recurrent configurations of a Chip-firing game (with a distinguished sink vertex) has been established for undirected graphs. ","authors_text":"K\\'evin Perrot, Trung Van Pham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-03T04:38:01Z","title":"Chip-firing game and partial Tutte polynomial for Eulerian digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0294","kind":"arxiv","version":5},"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":"sha256:6e56b442e19b636f761b89784d1d946601f776dcb357178f22f47ba91087814c","target":"record","created_at":"2026-05-18T03:12:22Z","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":"e177a91286947f19707d1b3eed61b74aa9df7a708c03992ba99518055b33bcbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-03T04:38:01Z","title_canon_sha256":"858ef4f9caa53a0adc55c965880e09bf87342fea7bdaa81dfe0d9fdff22eb304"},"schema_version":"1.0","source":{"id":"1306.0294","kind":"arxiv","version":5}},"canonical_sha256":"11c8f0dc975d3cf05a8c20da2e54432f36ba039ed8356a200746781e788b915f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11c8f0dc975d3cf05a8c20da2e54432f36ba039ed8356a200746781e788b915f","first_computed_at":"2026-05-18T03:12:22.035030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:22.035030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9aJYNWrt/pWNJJgJpwolmqhpMIfq2/b1WlR9qr7wLE2+JzGN51Zjm3/b+PZUb9EkrfTYBQ/MPZzWlVA3+tE2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:22.035968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0294","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e56b442e19b636f761b89784d1d946601f776dcb357178f22f47ba91087814c","sha256:22ffdd851d6db276741d57ce71c9c6da7a21ea1ce4cedd0d83b67a05e2a10a69"],"state_sha256":"9a8f71e3b5365fb680a2ba40aeff6d172ed19e5ec3f480e1a492de898947f87a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ac+XF1iPga1sIpdANNh2VI6Od+umqHjvAKV4AfUJWb9rK0suU0MLe+bCz7y8L8QqiF4ZILUgUfaJvqn3BiAfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T14:04:46.679118Z","bundle_sha256":"29aa81d43f9a75480fae3c767eb39fdc4990d3a53b45834231f3dd8125550ff3"}}