{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HY5TNARQ2TX6YRGGA2TZICZ53N","short_pith_number":"pith:HY5TNARQ","canonical_record":{"source":{"id":"1910.07913","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-16T12:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"1fbf3483e0599707a90d9680e74e8c8191d5a9b496c9495baf713330340b4435","abstract_canon_sha256":"d326e1936d23b0d9925d8f5fc2aeef0ad2c8228b412de97b9e8b6a7e28d8ac0b"},"schema_version":"1.0"},"canonical_sha256":"3e3b368230d4efec44c606a7940b3ddb5df876209d5381af27afb8059d68b3f6","source":{"kind":"arxiv","id":"1910.07913","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07913","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07913v5","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07913","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_12","alias_value":"HY5TNARQ2TX6","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_16","alias_value":"HY5TNARQ2TX6YRGG","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_8","alias_value":"HY5TNARQ","created_at":"2026-07-05T05:07:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HY5TNARQ2TX6YRGGA2TZICZ53N","target":"record","payload":{"canonical_record":{"source":{"id":"1910.07913","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-16T12:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"1fbf3483e0599707a90d9680e74e8c8191d5a9b496c9495baf713330340b4435","abstract_canon_sha256":"d326e1936d23b0d9925d8f5fc2aeef0ad2c8228b412de97b9e8b6a7e28d8ac0b"},"schema_version":"1.0"},"canonical_sha256":"3e3b368230d4efec44c606a7940b3ddb5df876209d5381af27afb8059d68b3f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:07:31.641090Z","signature_b64":"ZxCrSp75mb4h7mreClq0baegtZImO5nCzoNmH3IntwiU/3Ef8XWqL82rIADZWNaioVW0nDOdph5/VI/jExwRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3b368230d4efec44c606a7940b3ddb5df876209d5381af27afb8059d68b3f6","last_reissued_at":"2026-07-05T05:07:31.640723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:07:31.640723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.07913","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:07:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEKYPfEFjai0xfkREdPyczJQyZjBPkuH0IIplZOgfi7Zy3fURT+gWNH0IZZpGV75v/v8fXKYLx96bIi9ghazDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:45:47.692694Z"},"content_sha256":"c9ddc38874a6e042cebb1ae8eb5b7fca832442ce6435a01715077e481e963f28","schema_version":"1.0","event_id":"sha256:c9ddc38874a6e042cebb1ae8eb5b7fca832442ce6435a01715077e481e963f28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HY5TNARQ2TX6YRGGA2TZICZ53N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations and the foundations of mathematics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sam Sanders","submitted_at":"2019-10-16T12:57:53Z","abstract_excerpt":"The representation of mathematical objects in terms of (more) basic ones is part and parcel of (the foundations of) mathematics. In the usual foundations of mathematics, i.e. $\\textsf{ZFC}$ set theory, all mathematical objects are represented by sets, while ordinary, i.e. non-set theoretic, mathematics is represented in the more parsimonious language of second-order arithmetic. This paper deals with the latter representation for the rather basic case of continuous functions on the reals and Baire space. We show that the logical strength of basic theorems named after Tietze, Heine, and Weierstr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07913","kind":"arxiv","version":5},"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/1910.07913/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:07:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0QpJyfwlJlHiIbQgBkE0l/XJxakYfBLPg4H9IUk9KLV0Ml75lPw3ElHm2/mf/2qU5llZsRu7e1uai0B/DI2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:45:47.693908Z"},"content_sha256":"126197741395613988278377007e9d56eefda5c952e30fd5e469f8b8096a1164","schema_version":"1.0","event_id":"sha256:126197741395613988278377007e9d56eefda5c952e30fd5e469f8b8096a1164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/bundle.json","state_url":"https://pith.science/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T20:45:47Z","links":{"resolver":"https://pith.science/pith/HY5TNARQ2TX6YRGGA2TZICZ53N","bundle":"https://pith.science/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/bundle.json","state":"https://pith.science/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY5TNARQ2TX6YRGGA2TZICZ53N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HY5TNARQ2TX6YRGGA2TZICZ53N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d326e1936d23b0d9925d8f5fc2aeef0ad2c8228b412de97b9e8b6a7e28d8ac0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-16T12:57:53Z","title_canon_sha256":"1fbf3483e0599707a90d9680e74e8c8191d5a9b496c9495baf713330340b4435"},"schema_version":"1.0","source":{"id":"1910.07913","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07913","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07913v5","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07913","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_12","alias_value":"HY5TNARQ2TX6","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_16","alias_value":"HY5TNARQ2TX6YRGG","created_at":"2026-07-05T05:07:31Z"},{"alias_kind":"pith_short_8","alias_value":"HY5TNARQ","created_at":"2026-07-05T05:07:31Z"}],"graph_snapshots":[{"event_id":"sha256:126197741395613988278377007e9d56eefda5c952e30fd5e469f8b8096a1164","target":"graph","created_at":"2026-07-05T05:07:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.07913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The representation of mathematical objects in terms of (more) basic ones is part and parcel of (the foundations of) mathematics. In the usual foundations of mathematics, i.e. $\\textsf{ZFC}$ set theory, all mathematical objects are represented by sets, while ordinary, i.e. non-set theoretic, mathematics is represented in the more parsimonious language of second-order arithmetic. This paper deals with the latter representation for the rather basic case of continuous functions on the reals and Baire space. We show that the logical strength of basic theorems named after Tietze, Heine, and Weierstr","authors_text":"Sam Sanders","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-16T12:57:53Z","title":"Representations and the foundations of mathematics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07913","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c9ddc38874a6e042cebb1ae8eb5b7fca832442ce6435a01715077e481e963f28","target":"record","created_at":"2026-07-05T05:07:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d326e1936d23b0d9925d8f5fc2aeef0ad2c8228b412de97b9e8b6a7e28d8ac0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-10-16T12:57:53Z","title_canon_sha256":"1fbf3483e0599707a90d9680e74e8c8191d5a9b496c9495baf713330340b4435"},"schema_version":"1.0","source":{"id":"1910.07913","kind":"arxiv","version":5}},"canonical_sha256":"3e3b368230d4efec44c606a7940b3ddb5df876209d5381af27afb8059d68b3f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3b368230d4efec44c606a7940b3ddb5df876209d5381af27afb8059d68b3f6","first_computed_at":"2026-07-05T05:07:31.640723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:07:31.640723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZxCrSp75mb4h7mreClq0baegtZImO5nCzoNmH3IntwiU/3Ef8XWqL82rIADZWNaioVW0nDOdph5/VI/jExwRBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:07:31.641090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.07913","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9ddc38874a6e042cebb1ae8eb5b7fca832442ce6435a01715077e481e963f28","sha256:126197741395613988278377007e9d56eefda5c952e30fd5e469f8b8096a1164"],"state_sha256":"8ffa0f6cab6e499f80bfc930b44ac0fe7ba9689aae57dee33c8199131fb5d9ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAINXXI/lDpOKUdLBLKRX5q3XX+1IhXcz/ePKUQVnDC1EeC5DUxcgHogRzVdc4lpZ4MU43IOcElPK7hLcCmfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T20:45:47.699281Z","bundle_sha256":"e4828b6e666341abe3c05f488d8ecb6e9afe07e03f3c67e578b885d1c7088034"}}