{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:B3BIHDAS44LVJJ2WJXZUW6AZWT","short_pith_number":"pith:B3BIHDAS","schema_version":"1.0","canonical_sha256":"0ec2838c12e71754a7564df34b7819b4e986a2f3c9040be6ec971d643ee8beb2","source":{"kind":"arxiv","id":"1902.02404","version":1},"attestation_state":"computed","paper":{"title":"Flow-firing processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caroline Klivans, Pedro Felzenszwalb","submitted_at":"2019-02-06T21:42:48Z","abstract_excerpt":"We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted across the faces of the complex. For non-conservative initial configurations we show this process never terminates. For conservative initial flows we show the process terminates after a finite number of rerouting steps, but there are many possible final configurations reachable from a single initial state. Finally, for conservative initial "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.02404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-06T21:42:48Z","cross_cats_sorted":[],"title_canon_sha256":"9dd94e764acddb416c7e94f16916ad8d1c02a5601e6cbb585af8d9b041aa3dab","abstract_canon_sha256":"69fc95951fd36c70b55aa706bcf08657f2f8ebae7b8f670af68b25391f009cea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:33.470965Z","signature_b64":"KzpXguZ2sBKt2Q8732Kq5Npv5bpFdmfFa/ie0DZzq23sbRQRERu7U72BMcfDYSLfFEcodrEqcRRXsUDay+ZwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec2838c12e71754a7564df34b7819b4e986a2f3c9040be6ec971d643ee8beb2","last_reissued_at":"2026-05-17T23:54:33.470256Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:33.470256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flow-firing processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caroline Klivans, Pedro Felzenszwalb","submitted_at":"2019-02-06T21:42:48Z","abstract_excerpt":"We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted across the faces of the complex. For non-conservative initial configurations we show this process never terminates. For conservative initial flows we show the process terminates after a finite number of rerouting steps, but there are many possible final configurations reachable from a single initial state. Finally, for conservative initial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02404","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.02404","created_at":"2026-05-17T23:54:33.470376+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02404v1","created_at":"2026-05-17T23:54:33.470376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02404","created_at":"2026-05-17T23:54:33.470376+00:00"},{"alias_kind":"pith_short_12","alias_value":"B3BIHDAS44LV","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"B3BIHDAS44LVJJ2W","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"B3BIHDAS","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT","json":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT.json","graph_json":"https://pith.science/api/pith-number/B3BIHDAS44LVJJ2WJXZUW6AZWT/graph.json","events_json":"https://pith.science/api/pith-number/B3BIHDAS44LVJJ2WJXZUW6AZWT/events.json","paper":"https://pith.science/paper/B3BIHDAS"},"agent_actions":{"view_html":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT","download_json":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT.json","view_paper":"https://pith.science/paper/B3BIHDAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02404&json=true","fetch_graph":"https://pith.science/api/pith-number/B3BIHDAS44LVJJ2WJXZUW6AZWT/graph.json","fetch_events":"https://pith.science/api/pith-number/B3BIHDAS44LVJJ2WJXZUW6AZWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT/action/storage_attestation","attest_author":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT/action/author_attestation","sign_citation":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT/action/citation_signature","submit_replication":"https://pith.science/pith/B3BIHDAS44LVJJ2WJXZUW6AZWT/action/replication_record"}},"created_at":"2026-05-17T23:54:33.470376+00:00","updated_at":"2026-05-17T23:54:33.470376+00:00"}