{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:46GJMD3YNSX4B7YCC4STSQVKB4","short_pith_number":"pith:46GJMD3Y","canonical_record":{"source":{"id":"1504.03588","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-14T15:41:54Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"80e27841b9bc653da1e1f25048b247e94b62c28a32fb50b67b92f6f87f5e35d6","abstract_canon_sha256":"8d750125813fa3809dafba14dc2fb55ad69fb914c568f5fd0d8983f68bcf8ec6"},"schema_version":"1.0"},"canonical_sha256":"e78c960f786cafc0ff0217253942aa0f1ca87ebfb8c5a967d4e8b93fb41f74dc","source":{"kind":"arxiv","id":"1504.03588","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03588","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03588v3","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03588","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"46GJMD3YNSX4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"46GJMD3YNSX4B7YC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"46GJMD3Y","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:46GJMD3YNSX4B7YCC4STSQVKB4","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03588","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-14T15:41:54Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"80e27841b9bc653da1e1f25048b247e94b62c28a32fb50b67b92f6f87f5e35d6","abstract_canon_sha256":"8d750125813fa3809dafba14dc2fb55ad69fb914c568f5fd0d8983f68bcf8ec6"},"schema_version":"1.0"},"canonical_sha256":"e78c960f786cafc0ff0217253942aa0f1ca87ebfb8c5a967d4e8b93fb41f74dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.367916Z","signature_b64":"BJUwj7jTPQyQxEe/Tyr4x+jfNWcD4m/x8+3cKZPmKYfJVJKv1tWkkBoZaYQxvOmW8j8reJvB/HL7rHGPsAH3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e78c960f786cafc0ff0217253942aa0f1ca87ebfb8c5a967d4e8b93fb41f74dc","last_reissued_at":"2026-05-18T00:57:38.366855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.366855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03588","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CAA/hHGXCYqy1ogaXXnEZU2Dm/YbxvRm4WVTxP/cqJhWn33X/jpL0dDr7h+mrGSkXNd8JrExJ8HGfVGPkeFdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:30:02.707137Z"},"content_sha256":"709341c32d7d7aeb1d9695a02dd67b23388d8340450d737c974736947e7b2a5f","schema_version":"1.0","event_id":"sha256:709341c32d7d7aeb1d9695a02dd67b23388d8340450d737c974736947e7b2a5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:46GJMD3YNSX4B7YCC4STSQVKB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a noncommutative Brouwer fixed-point theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.QA","authors_text":"Ludwik Dabrowski","submitted_at":"2015-04-14T15:41:54Z","abstract_excerpt":"We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03588","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":""},"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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlNGPcWaM7spOIX2CqU/FbLOMhWQlFezYeWYBOUSr9wylBa+ETXqMjfB5ou5IXHosSbqwpXEB+9hC/+77yb7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:30:02.707509Z"},"content_sha256":"98b8a12d8810c9f48d6d00d65f76877a793edb3e93e9cff78e281ab49b3a47e1","schema_version":"1.0","event_id":"sha256:98b8a12d8810c9f48d6d00d65f76877a793edb3e93e9cff78e281ab49b3a47e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46GJMD3YNSX4B7YCC4STSQVKB4/bundle.json","state_url":"https://pith.science/pith/46GJMD3YNSX4B7YCC4STSQVKB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46GJMD3YNSX4B7YCC4STSQVKB4/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":"2026-06-12T08:30:02Z","links":{"resolver":"https://pith.science/pith/46GJMD3YNSX4B7YCC4STSQVKB4","bundle":"https://pith.science/pith/46GJMD3YNSX4B7YCC4STSQVKB4/bundle.json","state":"https://pith.science/pith/46GJMD3YNSX4B7YCC4STSQVKB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46GJMD3YNSX4B7YCC4STSQVKB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:46GJMD3YNSX4B7YCC4STSQVKB4","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":"8d750125813fa3809dafba14dc2fb55ad69fb914c568f5fd0d8983f68bcf8ec6","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-14T15:41:54Z","title_canon_sha256":"80e27841b9bc653da1e1f25048b247e94b62c28a32fb50b67b92f6f87f5e35d6"},"schema_version":"1.0","source":{"id":"1504.03588","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03588","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03588v3","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03588","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"46GJMD3YNSX4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"46GJMD3YNSX4B7YC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"46GJMD3Y","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:98b8a12d8810c9f48d6d00d65f76877a793edb3e93e9cff78e281ab49b3a47e1","target":"graph","created_at":"2026-05-18T00:57:38Z","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":"We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.","authors_text":"Ludwik Dabrowski","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-14T15:41:54Z","title":"Towards a noncommutative Brouwer fixed-point theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03588","kind":"arxiv","version":3},"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":"sha256:709341c32d7d7aeb1d9695a02dd67b23388d8340450d737c974736947e7b2a5f","target":"record","created_at":"2026-05-18T00:57:38Z","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":"8d750125813fa3809dafba14dc2fb55ad69fb914c568f5fd0d8983f68bcf8ec6","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-04-14T15:41:54Z","title_canon_sha256":"80e27841b9bc653da1e1f25048b247e94b62c28a32fb50b67b92f6f87f5e35d6"},"schema_version":"1.0","source":{"id":"1504.03588","kind":"arxiv","version":3}},"canonical_sha256":"e78c960f786cafc0ff0217253942aa0f1ca87ebfb8c5a967d4e8b93fb41f74dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e78c960f786cafc0ff0217253942aa0f1ca87ebfb8c5a967d4e8b93fb41f74dc","first_computed_at":"2026-05-18T00:57:38.366855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.366855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BJUwj7jTPQyQxEe/Tyr4x+jfNWcD4m/x8+3cKZPmKYfJVJKv1tWkkBoZaYQxvOmW8j8reJvB/HL7rHGPsAH3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.367916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03588","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:709341c32d7d7aeb1d9695a02dd67b23388d8340450d737c974736947e7b2a5f","sha256:98b8a12d8810c9f48d6d00d65f76877a793edb3e93e9cff78e281ab49b3a47e1"],"state_sha256":"08bd8f8828c25f1e8264c732020154788e87827bb44fd22083290ffa08f2e90e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W91MxYrSYLAry7BJe978FMWEk/9k8De0S66ZpkJtJRNjcgqo/pjTVcL1LuGFAUMUXpY0nZxQJ1Wrjf22BEOLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:30:02.709675Z","bundle_sha256":"e710f457ba02daebb0b885684ade8b95faec25cb2556422b88608bf485cd334a"}}