{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5SL5WBONXHBXE6ALDCWIT4MORR","short_pith_number":"pith:5SL5WBON","canonical_record":{"source":{"id":"1205.4540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-21T09:35:49Z","cross_cats_sorted":[],"title_canon_sha256":"9f710812dc34fe5898d66f4666f0a9ff181c74f2132ff7df19239ec098dbebe2","abstract_canon_sha256":"d7ee1b55d23b514a5c932c275a8ee30cfd2c1815b9e583e31aa2c8a63cfe5e3a"},"schema_version":"1.0"},"canonical_sha256":"ec97db05cdb9c372780b18ac89f18e8c644d863c68f784a9882bda882beeea92","source":{"kind":"arxiv","id":"1205.4540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4540","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4540v1","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4540","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"5SL5WBONXHBX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5SL5WBONXHBXE6AL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5SL5WBON","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5SL5WBONXHBXE6ALDCWIT4MORR","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-21T09:35:49Z","cross_cats_sorted":[],"title_canon_sha256":"9f710812dc34fe5898d66f4666f0a9ff181c74f2132ff7df19239ec098dbebe2","abstract_canon_sha256":"d7ee1b55d23b514a5c932c275a8ee30cfd2c1815b9e583e31aa2c8a63cfe5e3a"},"schema_version":"1.0"},"canonical_sha256":"ec97db05cdb9c372780b18ac89f18e8c644d863c68f784a9882bda882beeea92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:12.970684Z","signature_b64":"jThAUf4JIa+sRwudhrBFTbMLOqyMQKY2KScdX1JfCmDIKswOdl8S9IwhiSNHkxtS0RXgaVyQaZOCXgwPCYGMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec97db05cdb9c372780b18ac89f18e8c644d863c68f784a9882bda882beeea92","last_reissued_at":"2026-05-18T03:55:12.970256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:12.970256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4540","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ckXrMZOYXZqa7CU9oE0NnL0S9oZkwaCqv+ZaDyK7P2INf+xXjOrgzEhlP3L5bcjSsevvcPnc2ldgM4aSYBfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:42:50.303631Z"},"content_sha256":"4f414dc03291832286c8b6cd076d58cc863089aed3b505335f635885859c4dc5","schema_version":"1.0","event_id":"sha256:4f414dc03291832286c8b6cd076d58cc863089aed3b505335f635885859c4dc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5SL5WBONXHBXE6ALDCWIT4MORR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Brouwer fixed point theorem and the Borsuk--Ulam theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Anthony Carbery","submitted_at":"2012-05-21T09:35:49Z","abstract_excerpt":"These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone with a knowledge of basic point-set topology and several variable calculus. Some of the argument relies upon previous ideas of Shchepin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4540","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLqphPh6VKyvf86BUj1KIJVHUiP0fH6+l98hBx3iWLISqnY9s2hJJw4j8kcHTBpjinRPPWXUUhPft5frYk/RCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:42:50.304305Z"},"content_sha256":"ee68178ac771df2b6a75e6753bc42d047f779940ec9b966252c3446f676217fa","schema_version":"1.0","event_id":"sha256:ee68178ac771df2b6a75e6753bc42d047f779940ec9b966252c3446f676217fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5SL5WBONXHBXE6ALDCWIT4MORR/bundle.json","state_url":"https://pith.science/pith/5SL5WBONXHBXE6ALDCWIT4MORR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5SL5WBONXHBXE6ALDCWIT4MORR/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":"2026-06-07T20:42:50Z","links":{"resolver":"https://pith.science/pith/5SL5WBONXHBXE6ALDCWIT4MORR","bundle":"https://pith.science/pith/5SL5WBONXHBXE6ALDCWIT4MORR/bundle.json","state":"https://pith.science/pith/5SL5WBONXHBXE6ALDCWIT4MORR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5SL5WBONXHBXE6ALDCWIT4MORR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5SL5WBONXHBXE6ALDCWIT4MORR","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":"d7ee1b55d23b514a5c932c275a8ee30cfd2c1815b9e583e31aa2c8a63cfe5e3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-21T09:35:49Z","title_canon_sha256":"9f710812dc34fe5898d66f4666f0a9ff181c74f2132ff7df19239ec098dbebe2"},"schema_version":"1.0","source":{"id":"1205.4540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4540","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4540v1","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4540","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"5SL5WBONXHBX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5SL5WBONXHBXE6AL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5SL5WBON","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:ee68178ac771df2b6a75e6753bc42d047f779940ec9b966252c3446f676217fa","target":"graph","created_at":"2026-05-18T03:55:12Z","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"},"paper":{"abstract_excerpt":"These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone with a knowledge of basic point-set topology and several variable calculus. Some of the argument relies upon previous ideas of Shchepin.","authors_text":"Anthony Carbery","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-21T09:35:49Z","title":"The Brouwer fixed point theorem and the Borsuk--Ulam theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4540","kind":"arxiv","version":1},"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":"sha256:4f414dc03291832286c8b6cd076d58cc863089aed3b505335f635885859c4dc5","target":"record","created_at":"2026-05-18T03:55:12Z","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":"d7ee1b55d23b514a5c932c275a8ee30cfd2c1815b9e583e31aa2c8a63cfe5e3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-21T09:35:49Z","title_canon_sha256":"9f710812dc34fe5898d66f4666f0a9ff181c74f2132ff7df19239ec098dbebe2"},"schema_version":"1.0","source":{"id":"1205.4540","kind":"arxiv","version":1}},"canonical_sha256":"ec97db05cdb9c372780b18ac89f18e8c644d863c68f784a9882bda882beeea92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec97db05cdb9c372780b18ac89f18e8c644d863c68f784a9882bda882beeea92","first_computed_at":"2026-05-18T03:55:12.970256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:12.970256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jThAUf4JIa+sRwudhrBFTbMLOqyMQKY2KScdX1JfCmDIKswOdl8S9IwhiSNHkxtS0RXgaVyQaZOCXgwPCYGMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:12.970684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f414dc03291832286c8b6cd076d58cc863089aed3b505335f635885859c4dc5","sha256:ee68178ac771df2b6a75e6753bc42d047f779940ec9b966252c3446f676217fa"],"state_sha256":"51cc1cd423deeec383f1ebf2de344311ccc84ad10ecbbf3cd80ebad70647a107"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuPOaQWOLgA2YtgOjtqi/VcKb8QiMC5x/2lZ/mWPYbY0rSQgnTK3eVGTul7tzEU+KQv/TIT70cFSrMdLHFiHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:42:50.307983Z","bundle_sha256":"05861a1bc59438299ef4e318527bfa680c4bca6d48f009d0364a9e8208feba96"}}