{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:VOSM3ZL3MQCK6HLUQCZQZJY3RQ","short_pith_number":"pith:VOSM3ZL3","schema_version":"1.0","canonical_sha256":"aba4cde57b6404af1d7480b30ca71b8c19735d95fbaa1395dac84a9a75c6cc1b","source":{"kind":"arxiv","id":"2107.14078","version":2},"attestation_state":"computed","paper":{"title":"Volume growth for infinite graphs and translation surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Paul Colognese","submitted_at":"2021-07-29T15:09:10Z","abstract_excerpt":"In this note we give asymptotic estimates for the volume growth associated to suitable infinite graphs. Our main application is to give an asymptotic estimate for volume growth associated to translation surfaces."},"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":"2107.14078","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-07-29T15:09:10Z","cross_cats_sorted":[],"title_canon_sha256":"214f796e4e133b3aff8fc85bb39e26c9cad85aacb3004cb3840c2456c3989499","abstract_canon_sha256":"d3f344e6669e3ff17cd0317962ac1ff03e75d411998d7394b7896ae2e2c78696"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:57.870149Z","signature_b64":"cvjdtmTSLnCvn1rA4WV4mZPdULusiUna1+t5vzYSx2u4LRPBCkXJx7jvsGkTuAEP2CPXuYPKApYCIs7c82O5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aba4cde57b6404af1d7480b30ca71b8c19735d95fbaa1395dac84a9a75c6cc1b","last_reissued_at":"2026-07-05T03:01:57.869742Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:57.869742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume growth for infinite graphs and translation surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Paul Colognese","submitted_at":"2021-07-29T15:09:10Z","abstract_excerpt":"In this note we give asymptotic estimates for the volume growth associated to suitable infinite graphs. Our main application is to give an asymptotic estimate for volume growth associated to translation surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14078","kind":"arxiv","version":2},"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/2107.14078/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":"2107.14078","created_at":"2026-07-05T03:01:57.869798+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.14078v2","created_at":"2026-07-05T03:01:57.869798+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.14078","created_at":"2026-07-05T03:01:57.869798+00:00"},{"alias_kind":"pith_short_12","alias_value":"VOSM3ZL3MQCK","created_at":"2026-07-05T03:01:57.869798+00:00"},{"alias_kind":"pith_short_16","alias_value":"VOSM3ZL3MQCK6HLU","created_at":"2026-07-05T03:01:57.869798+00:00"},{"alias_kind":"pith_short_8","alias_value":"VOSM3ZL3","created_at":"2026-07-05T03:01:57.869798+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/VOSM3ZL3MQCK6HLUQCZQZJY3RQ","json":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ.json","graph_json":"https://pith.science/api/pith-number/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/graph.json","events_json":"https://pith.science/api/pith-number/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/events.json","paper":"https://pith.science/paper/VOSM3ZL3"},"agent_actions":{"view_html":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ","download_json":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ.json","view_paper":"https://pith.science/paper/VOSM3ZL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.14078&json=true","fetch_graph":"https://pith.science/api/pith-number/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/action/storage_attestation","attest_author":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/action/author_attestation","sign_citation":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/action/citation_signature","submit_replication":"https://pith.science/pith/VOSM3ZL3MQCK6HLUQCZQZJY3RQ/action/replication_record"}},"created_at":"2026-07-05T03:01:57.869798+00:00","updated_at":"2026-07-05T03:01:57.869798+00:00"}