{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H6D3DDHJFMCHZ2RT6F4OD4VMDZ","short_pith_number":"pith:H6D3DDHJ","canonical_record":{"source":{"id":"1602.01759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-02-04T17:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"6f9fa8847729f064a66daf868f19b76b746d2203e38d3f2d72f04c8318df8aaa","abstract_canon_sha256":"99c1d251b076cbe8d989224d1a3e948f92b96893bac05be384251485ba9d1436"},"schema_version":"1.0"},"canonical_sha256":"3f87b18ce92b047cea33f178e1f2ac1e67666b6aaa4246c20cda1565f2cd07d1","source":{"kind":"arxiv","id":"1602.01759","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01759","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01759v1","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01759","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"H6D3DDHJFMCH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H6D3DDHJFMCHZ2RT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H6D3DDHJ","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H6D3DDHJFMCHZ2RT6F4OD4VMDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-02-04T17:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"6f9fa8847729f064a66daf868f19b76b746d2203e38d3f2d72f04c8318df8aaa","abstract_canon_sha256":"99c1d251b076cbe8d989224d1a3e948f92b96893bac05be384251485ba9d1436"},"schema_version":"1.0"},"canonical_sha256":"3f87b18ce92b047cea33f178e1f2ac1e67666b6aaa4246c20cda1565f2cd07d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:18.167442Z","signature_b64":"hHpKo88xjKAVn3nnMUk4VJ766ly0lE4VrRWdLEyxyc0FUk1qalb+OY5AkKcY+ct+cXU1QM6rrFQA3rvGx14cCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f87b18ce92b047cea33f178e1f2ac1e67666b6aaa4246c20cda1565f2cd07d1","last_reissued_at":"2026-05-18T01:21:18.166911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:18.166911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01759","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":"2026-05-18T01:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O72wjpyceNseEQf2wCBPHYgPAo/SVubdlNzvV92j5M6CT7xibn6t5g4+9uoGp2t63BOsU1qpesOjMyKrVasDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:16:23.037926Z"},"content_sha256":"af60890f48c4a0f0bd7a5eca54a42a4392c257942ee35d33cf5f3954f141425e","schema_version":"1.0","event_id":"sha256:af60890f48c4a0f0bd7a5eca54a42a4392c257942ee35d33cf5f3954f141425e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H6D3DDHJFMCHZ2RT6F4OD4VMDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Category Free Category Theory and Its Philosophical Implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Michael Heller","submitted_at":"2016-02-04T17:39:37Z","abstract_excerpt":"There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely eliminated. Category theory seems to be the correct mathematical theory for clarifying conceptual possibilities in this respect. In this theory, objects acquire their identity either by definition, when in defining category we postulate the existence of objects, or formally by the existence of identity morphisms. We show that it is perfectly possible to get "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01759","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":"2026-05-18T01:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BCVoW1uoyoKhz1buI2SoP6MW0PeUXb4rjHINgPpVGCxAJCNFh8IRLX5GNNYQ3AgMcw4A0rUHQhAiMIyusrF+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:16:23.038258Z"},"content_sha256":"d99e1c601d88798af016255411b6973d0ec24a22154737dd7f9203153c7fd038","schema_version":"1.0","event_id":"sha256:d99e1c601d88798af016255411b6973d0ec24a22154737dd7f9203153c7fd038"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/bundle.json","state_url":"https://pith.science/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/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":"2026-06-29T08:16:23Z","links":{"resolver":"https://pith.science/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ","bundle":"https://pith.science/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/bundle.json","state":"https://pith.science/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6D3DDHJFMCHZ2RT6F4OD4VMDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H6D3DDHJFMCHZ2RT6F4OD4VMDZ","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":"99c1d251b076cbe8d989224d1a3e948f92b96893bac05be384251485ba9d1436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-02-04T17:39:37Z","title_canon_sha256":"6f9fa8847729f064a66daf868f19b76b746d2203e38d3f2d72f04c8318df8aaa"},"schema_version":"1.0","source":{"id":"1602.01759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01759","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01759v1","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01759","created_at":"2026-05-18T01:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"H6D3DDHJFMCH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H6D3DDHJFMCHZ2RT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H6D3DDHJ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d99e1c601d88798af016255411b6973d0ec24a22154737dd7f9203153c7fd038","target":"graph","created_at":"2026-05-18T01:21:18Z","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":"There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely eliminated. Category theory seems to be the correct mathematical theory for clarifying conceptual possibilities in this respect. In this theory, objects acquire their identity either by definition, when in defining category we postulate the existence of objects, or formally by the existence of identity morphisms. We show that it is perfectly possible to get ","authors_text":"Michael Heller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-02-04T17:39:37Z","title":"Category Free Category Theory and Its Philosophical Implications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01759","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:af60890f48c4a0f0bd7a5eca54a42a4392c257942ee35d33cf5f3954f141425e","target":"record","created_at":"2026-05-18T01:21:18Z","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":"99c1d251b076cbe8d989224d1a3e948f92b96893bac05be384251485ba9d1436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-02-04T17:39:37Z","title_canon_sha256":"6f9fa8847729f064a66daf868f19b76b746d2203e38d3f2d72f04c8318df8aaa"},"schema_version":"1.0","source":{"id":"1602.01759","kind":"arxiv","version":1}},"canonical_sha256":"3f87b18ce92b047cea33f178e1f2ac1e67666b6aaa4246c20cda1565f2cd07d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f87b18ce92b047cea33f178e1f2ac1e67666b6aaa4246c20cda1565f2cd07d1","first_computed_at":"2026-05-18T01:21:18.166911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:18.166911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHpKo88xjKAVn3nnMUk4VJ766ly0lE4VrRWdLEyxyc0FUk1qalb+OY5AkKcY+ct+cXU1QM6rrFQA3rvGx14cCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:18.167442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af60890f48c4a0f0bd7a5eca54a42a4392c257942ee35d33cf5f3954f141425e","sha256:d99e1c601d88798af016255411b6973d0ec24a22154737dd7f9203153c7fd038"],"state_sha256":"a7b076436e44f1c2d094d4061a662bc2063e7f42aab49696260972e02d92b486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCjh9LixrnK5LI498PrYTcCs1x6dPVgpZDXEY14171SROrkHY2OlfLEXQ0J+Byqv5Zj8Vn/XAWhJEtrDwWL1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:16:23.040017Z","bundle_sha256":"0d1d1842f6c25ba239f5f25f9d1ec9aecaa78e64a72512082f57ec1f63ccae14"}}