{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IZDJAFGTLC6QYJOFWNHBKQLTN6","short_pith_number":"pith:IZDJAFGT","schema_version":"1.0","canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","source":{"kind":"arxiv","id":"1008.4887","version":1},"attestation_state":"computed","paper":{"title":"Bounded geometry, growth and topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pierre Pansu (DMA), Renata Grimaldi (DMMM)","submitted_at":"2010-08-28T19:39:25Z","abstract_excerpt":"We characterize functions which are growth types of Riemannian manifolds of bounded geometry."},"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":"1008.4887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-28T19:39:25Z","cross_cats_sorted":[],"title_canon_sha256":"5182d4cf229e7bcc04fbcf5d9661f6a1810974c9343e8d6e7e9294527b7b4e61","abstract_canon_sha256":"8a9bc549ad6ac947b78331ae4944f1ab3f716075b5375bf0bc18aa4916c9988b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:43.492575Z","signature_b64":"CF7M08SBsPAY2JGcP0gRQo6k0dY39tp/nmTswTOB7AzZhUWwvfrgz6B04ElUNAuMMujssWECI9kAMdgUH2cLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46469014d358bd0c25c5b34e1541736f9556cb755f7699a574cc3239a55f2e37","last_reissued_at":"2026-05-18T04:41:43.492061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:43.492061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded geometry, growth and topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pierre Pansu (DMA), Renata Grimaldi (DMMM)","submitted_at":"2010-08-28T19:39:25Z","abstract_excerpt":"We characterize functions which are growth types of Riemannian manifolds of bounded geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4887","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":"1008.4887","created_at":"2026-05-18T04:41:43.492140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4887v1","created_at":"2026-05-18T04:41:43.492140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4887","created_at":"2026-05-18T04:41:43.492140+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZDJAFGTLC6Q","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZDJAFGTLC6QYJOF","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZDJAFGT","created_at":"2026-05-18T12:26:09.077623+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/IZDJAFGTLC6QYJOFWNHBKQLTN6","json":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6.json","graph_json":"https://pith.science/api/pith-number/IZDJAFGTLC6QYJOFWNHBKQLTN6/graph.json","events_json":"https://pith.science/api/pith-number/IZDJAFGTLC6QYJOFWNHBKQLTN6/events.json","paper":"https://pith.science/paper/IZDJAFGT"},"agent_actions":{"view_html":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6","download_json":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6.json","view_paper":"https://pith.science/paper/IZDJAFGT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4887&json=true","fetch_graph":"https://pith.science/api/pith-number/IZDJAFGTLC6QYJOFWNHBKQLTN6/graph.json","fetch_events":"https://pith.science/api/pith-number/IZDJAFGTLC6QYJOFWNHBKQLTN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/action/storage_attestation","attest_author":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/action/author_attestation","sign_citation":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/action/citation_signature","submit_replication":"https://pith.science/pith/IZDJAFGTLC6QYJOFWNHBKQLTN6/action/replication_record"}},"created_at":"2026-05-18T04:41:43.492140+00:00","updated_at":"2026-05-18T04:41:43.492140+00:00"}