{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MOFUEIIUAIWI6UGGBOJZXUOFMT","short_pith_number":"pith:MOFUEIIU","schema_version":"1.0","canonical_sha256":"638b422114022c8f50c60b939bd1c564c47e944f0d367bb31d957647ecda1691","source":{"kind":"arxiv","id":"2501.06675","version":1},"attestation_state":"computed","paper":{"title":"Chip-Firing on Infinite $k$-ary Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Albert Xu, Anirudh Pulugurtha, Dillan Agrawal, Dohun Kim, Gordon Redwine, Jate Greene, Rajarshi Mandal, Selena Ge, Soham Samanta, Tanish Parida, Tanya Khovanova","submitted_at":"2025-01-12T00:31:42Z","abstract_excerpt":"We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires."},"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":"2501.06675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-12T00:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"b9f45daf2daf251ade8dc10301245d55953bb1837892c41aa7fb545f2e0c3021","abstract_canon_sha256":"824b365d4a03e67ddfb81c31ae621d060cb02eb2533ce2c575dffad227fc72f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:08.437250Z","signature_b64":"753XLvRAYUFkc9U898guvo5m6iL9kM/DL9ChTchifRN/7lLpFVSgWDULLQ/iiT7WgEtEvPMgXsciQAn7hBtNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"638b422114022c8f50c60b939bd1c564c47e944f0d367bb31d957647ecda1691","last_reissued_at":"2026-07-05T10:00:08.436821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:08.436821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chip-Firing on Infinite $k$-ary Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Albert Xu, Anirudh Pulugurtha, Dillan Agrawal, Dohun Kim, Gordon Redwine, Jate Greene, Rajarshi Mandal, Selena Ge, Soham Samanta, Tanish Parida, Tanya Khovanova","submitted_at":"2025-01-12T00:31:42Z","abstract_excerpt":"We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06675","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/2501.06675/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.06675","created_at":"2026-07-05T10:00:08.436878+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.06675v1","created_at":"2026-07-05T10:00:08.436878+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06675","created_at":"2026-07-05T10:00:08.436878+00:00"},{"alias_kind":"pith_short_12","alias_value":"MOFUEIIUAIWI","created_at":"2026-07-05T10:00:08.436878+00:00"},{"alias_kind":"pith_short_16","alias_value":"MOFUEIIUAIWI6UGG","created_at":"2026-07-05T10:00:08.436878+00:00"},{"alias_kind":"pith_short_8","alias_value":"MOFUEIIU","created_at":"2026-07-05T10:00:08.436878+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/MOFUEIIUAIWI6UGGBOJZXUOFMT","json":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT.json","graph_json":"https://pith.science/api/pith-number/MOFUEIIUAIWI6UGGBOJZXUOFMT/graph.json","events_json":"https://pith.science/api/pith-number/MOFUEIIUAIWI6UGGBOJZXUOFMT/events.json","paper":"https://pith.science/paper/MOFUEIIU"},"agent_actions":{"view_html":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT","download_json":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT.json","view_paper":"https://pith.science/paper/MOFUEIIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.06675&json=true","fetch_graph":"https://pith.science/api/pith-number/MOFUEIIUAIWI6UGGBOJZXUOFMT/graph.json","fetch_events":"https://pith.science/api/pith-number/MOFUEIIUAIWI6UGGBOJZXUOFMT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT/action/storage_attestation","attest_author":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT/action/author_attestation","sign_citation":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT/action/citation_signature","submit_replication":"https://pith.science/pith/MOFUEIIUAIWI6UGGBOJZXUOFMT/action/replication_record"}},"created_at":"2026-07-05T10:00:08.436878+00:00","updated_at":"2026-07-05T10:00:08.436878+00:00"}