{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EVF475MBD7TYREMZ4ZUMPA5BV6","short_pith_number":"pith:EVF475MB","canonical_record":{"source":{"id":"1512.06417","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-20T18:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"f0fccc9a573c7e4864ce6c66feac1d29be2a9c2e7ce0c01d6aa97c6f68b6fabc","abstract_canon_sha256":"c8dc80c924a3e7b8c81aa06b41ffe6cfefde19d7f59d25037259649715bda4df"},"schema_version":"1.0"},"canonical_sha256":"254bcff5811fe7889199e668c783a1afbd6e6e2dc9e89f9c372e7612644c588b","source":{"kind":"arxiv","id":"1512.06417","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06417","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06417v3","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06417","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"EVF475MBD7TY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EVF475MBD7TYREMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EVF475MB","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EVF475MBD7TYREMZ4ZUMPA5BV6","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06417","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-20T18:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"f0fccc9a573c7e4864ce6c66feac1d29be2a9c2e7ce0c01d6aa97c6f68b6fabc","abstract_canon_sha256":"c8dc80c924a3e7b8c81aa06b41ffe6cfefde19d7f59d25037259649715bda4df"},"schema_version":"1.0"},"canonical_sha256":"254bcff5811fe7889199e668c783a1afbd6e6e2dc9e89f9c372e7612644c588b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:05.585892Z","signature_b64":"Fca1THIPk8vjdegSzfClp4jDOlp+Ync2q5Tyc7f4kHSgyV5wbb63GwK/UwsygOXMsgTWtRMHKsupsncddBzFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"254bcff5811fe7889199e668c783a1afbd6e6e2dc9e89f9c372e7612644c588b","last_reissued_at":"2026-05-18T01:22:05.585407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:05.585407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06417","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":"2026-05-18T01:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AOH3hn6YnXaqj6pQKWG8Y1zc4g+xK6IBavBqFQTazaWYbZ8M6DRX4pBJPj4rkgSQPN8jicfEoQreyGNoCMDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:34:51.363462Z"},"content_sha256":"8dc044d8a74e876b302a9e4dffe0236ee618afe252e8a11fcc8c1ac45f38f6f4","schema_version":"1.0","event_id":"sha256:8dc044d8a74e876b302a9e4dffe0236ee618afe252e8a11fcc8c1ac45f38f6f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EVF475MBD7TYREMZ4ZUMPA5BV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delta Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis H. Kauffman, Pedro Lopes, Slavik Jablan","submitted_at":"2015-12-20T18:10:24Z","abstract_excerpt":"We call a Delta Diagram any diagram of a knot or link whose regions (including the unbounded one) have 3, 4, or 5 sides. We prove that any knot or link admits a delta diagram. We define and estimate combinatorial link invariants stemming from this definition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06417","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":"2026-05-18T01:22:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XeZuGH+P23xTcCapNDY9+yDS8quJNiwRyEhh6PSYXlZnrdehJKTSSauSkwAzJmKmXHBDCjhFCY5ybHPivAVeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:34:51.364157Z"},"content_sha256":"3151fe032237dfef51fbbff0463e5182e66a976614185f7c447903a1e9ffae25","schema_version":"1.0","event_id":"sha256:3151fe032237dfef51fbbff0463e5182e66a976614185f7c447903a1e9ffae25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/bundle.json","state_url":"https://pith.science/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/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":"2026-06-09T08:34:51Z","links":{"resolver":"https://pith.science/pith/EVF475MBD7TYREMZ4ZUMPA5BV6","bundle":"https://pith.science/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/bundle.json","state":"https://pith.science/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVF475MBD7TYREMZ4ZUMPA5BV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EVF475MBD7TYREMZ4ZUMPA5BV6","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":"c8dc80c924a3e7b8c81aa06b41ffe6cfefde19d7f59d25037259649715bda4df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-20T18:10:24Z","title_canon_sha256":"f0fccc9a573c7e4864ce6c66feac1d29be2a9c2e7ce0c01d6aa97c6f68b6fabc"},"schema_version":"1.0","source":{"id":"1512.06417","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06417","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06417v3","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06417","created_at":"2026-05-18T01:22:05Z"},{"alias_kind":"pith_short_12","alias_value":"EVF475MBD7TY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EVF475MBD7TYREMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EVF475MB","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:3151fe032237dfef51fbbff0463e5182e66a976614185f7c447903a1e9ffae25","target":"graph","created_at":"2026-05-18T01:22:05Z","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 call a Delta Diagram any diagram of a knot or link whose regions (including the unbounded one) have 3, 4, or 5 sides. We prove that any knot or link admits a delta diagram. We define and estimate combinatorial link invariants stemming from this definition.","authors_text":"Louis H. Kauffman, Pedro Lopes, Slavik Jablan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-20T18:10:24Z","title":"Delta Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06417","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":"sha256:8dc044d8a74e876b302a9e4dffe0236ee618afe252e8a11fcc8c1ac45f38f6f4","target":"record","created_at":"2026-05-18T01:22:05Z","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":"c8dc80c924a3e7b8c81aa06b41ffe6cfefde19d7f59d25037259649715bda4df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-20T18:10:24Z","title_canon_sha256":"f0fccc9a573c7e4864ce6c66feac1d29be2a9c2e7ce0c01d6aa97c6f68b6fabc"},"schema_version":"1.0","source":{"id":"1512.06417","kind":"arxiv","version":3}},"canonical_sha256":"254bcff5811fe7889199e668c783a1afbd6e6e2dc9e89f9c372e7612644c588b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"254bcff5811fe7889199e668c783a1afbd6e6e2dc9e89f9c372e7612644c588b","first_computed_at":"2026-05-18T01:22:05.585407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:05.585407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fca1THIPk8vjdegSzfClp4jDOlp+Ync2q5Tyc7f4kHSgyV5wbb63GwK/UwsygOXMsgTWtRMHKsupsncddBzFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:05.585892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06417","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dc044d8a74e876b302a9e4dffe0236ee618afe252e8a11fcc8c1ac45f38f6f4","sha256:3151fe032237dfef51fbbff0463e5182e66a976614185f7c447903a1e9ffae25"],"state_sha256":"6168fa87ba916ec50f23942a3acc1c6d293d131a010b54bb8706627ade9773df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaNHy/gRdut7mpqVe0x7h488l14GXSRLhoa7icUtdKv++tNW8LXZREcYzTrJ6j5FmTMGB7dZMRWrRY1/5cdBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:34:51.367953Z","bundle_sha256":"61e50b1ef246a118c98ee4672e19147ffbff546d4c9f2dabc93a179c06c4bb49"}}