{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:623WO25NRG2AYTAHAZQNT4AAKP","short_pith_number":"pith:623WO25N","schema_version":"1.0","canonical_sha256":"f6b7676bad89b40c4c070660d9f00053c8c99fc8f62a184353d8811c1e64db48","source":{"kind":"arxiv","id":"math/0411418","version":3},"attestation_state":"computed","paper":{"title":"How real are real numbers?","license":"","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"G. J. Chaitin (IBM Research)","submitted_at":"2004-11-18T22:35:07Z","abstract_excerpt":"We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956)."},"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":"math/0411418","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.HO","submitted_at":"2004-11-18T22:35:07Z","cross_cats_sorted":[],"title_canon_sha256":"16fbe08fa6c2cabcd8f73eb1da7c0a96718479ae2bebe831844cda3ca7876c19","abstract_canon_sha256":"f509fc96d05edefba929a3567ce966af5df1b13ac121f2c00c98a6a9631d7584"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:23.238238Z","signature_b64":"uHBzzKNhfset24qO4mccLf4FzVCkY8naF7fCjBuZsQmGlwHv17nd79gdLLrv76DzgC4CQxa7bJDkWVGg33gADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b7676bad89b40c4c070660d9f00053c8c99fc8f62a184353d8811c1e64db48","last_reissued_at":"2026-07-04T14:39:23.237766Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:23.237766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How real are real numbers?","license":"","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"G. J. Chaitin (IBM Research)","submitted_at":"2004-11-18T22:35:07Z","abstract_excerpt":"We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411418","kind":"arxiv","version":3},"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/math/0411418/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":"math/0411418","created_at":"2026-07-04T14:39:23.237823+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411418v3","created_at":"2026-07-04T14:39:23.237823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411418","created_at":"2026-07-04T14:39:23.237823+00:00"},{"alias_kind":"pith_short_12","alias_value":"623WO25NRG2A","created_at":"2026-07-04T14:39:23.237823+00:00"},{"alias_kind":"pith_short_16","alias_value":"623WO25NRG2AYTAH","created_at":"2026-07-04T14:39:23.237823+00:00"},{"alias_kind":"pith_short_8","alias_value":"623WO25N","created_at":"2026-07-04T14:39:23.237823+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/623WO25NRG2AYTAHAZQNT4AAKP","json":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP.json","graph_json":"https://pith.science/api/pith-number/623WO25NRG2AYTAHAZQNT4AAKP/graph.json","events_json":"https://pith.science/api/pith-number/623WO25NRG2AYTAHAZQNT4AAKP/events.json","paper":"https://pith.science/paper/623WO25N"},"agent_actions":{"view_html":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP","download_json":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP.json","view_paper":"https://pith.science/paper/623WO25N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411418&json=true","fetch_graph":"https://pith.science/api/pith-number/623WO25NRG2AYTAHAZQNT4AAKP/graph.json","fetch_events":"https://pith.science/api/pith-number/623WO25NRG2AYTAHAZQNT4AAKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP/action/storage_attestation","attest_author":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP/action/author_attestation","sign_citation":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP/action/citation_signature","submit_replication":"https://pith.science/pith/623WO25NRG2AYTAHAZQNT4AAKP/action/replication_record"}},"created_at":"2026-07-04T14:39:23.237823+00:00","updated_at":"2026-07-04T14:39:23.237823+00:00"}