{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:7VYBYGUSYNQPS3WT4Y3UBPHSTZ","short_pith_number":"pith:7VYBYGUS","canonical_record":{"source":{"id":"math/0210119","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2002-10-08T13:54:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8bf6d0d216feb133c218dc5519d56040b0506e4347e2a5ba162a32e00ab9b6a0","abstract_canon_sha256":"24c9d34c8b13cb77502b780ff3c8bdb6b06f09bb7abb5777456b9012298fbab9"},"schema_version":"1.0"},"canonical_sha256":"fd701c1a92c360f96ed3e63740bcf29e5048cb93269d8fad63b73a2574d7799a","source":{"kind":"arxiv","id":"math/0210119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210119","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210119v1","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210119","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"7VYBYGUSYNQP","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_16","alias_value":"7VYBYGUSYNQPS3WT","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_8","alias_value":"7VYBYGUS","created_at":"2026-07-04T14:36:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:7VYBYGUSYNQPS3WT4Y3UBPHSTZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0210119","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2002-10-08T13:54:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8bf6d0d216feb133c218dc5519d56040b0506e4347e2a5ba162a32e00ab9b6a0","abstract_canon_sha256":"24c9d34c8b13cb77502b780ff3c8bdb6b06f09bb7abb5777456b9012298fbab9"},"schema_version":"1.0"},"canonical_sha256":"fd701c1a92c360f96ed3e63740bcf29e5048cb93269d8fad63b73a2574d7799a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:37.159490Z","signature_b64":"sL4Kp1F20vy3bajkUY7Og0cHpTCZK3A8TUjNKD21wyxBxj67dj1UHpDz1RweuemgkFxQOxhTFzX/88R71QgkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd701c1a92c360f96ed3e63740bcf29e5048cb93269d8fad63b73a2574d7799a","last_reissued_at":"2026-07-04T14:36:37.159078Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:37.159078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0210119","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":"2026-07-04T14:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmonvxKw2H3qLRE3lCxX/JoQNCxQe5AudZCGBLkUFw32HzsN+i0OdFMAATFJAublshdkwgxbsAulVvKIozhMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:42:56.767895Z"},"content_sha256":"d0ff3b2062dc573e22de08f241e64d565bd713f178faad6e1b3a570b54500d98","schema_version":"1.0","event_id":"sha256:d0ff3b2062dc573e22de08f241e64d565bd713f178faad6e1b3a570b54500d98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:7VYBYGUSYNQPS3WT4Y3UBPHSTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Tobias H. Colding, William P. Minicozzi II","submitted_at":"2002-10-08T13:54:17Z","abstract_excerpt":"This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in $\\RR^3$. This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see [CM15] for discussion of the local case and [CM13], [CM14] where we have surveyed our results about embedded minimal disks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210119","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0210119/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":"2026-07-04T14:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2QAs36WFwks5ZcyZKmXbhR4il6ZIjn186uaUlAfsHs70E3tOq3jm54T6uDVpYNfYfjdC/ibIEfkkNX20o+BBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T04:42:56.768393Z"},"content_sha256":"2db00b9867bb2d867a2d2f43cce94b130291e45ac8f810aea7b6042ed818aade","schema_version":"1.0","event_id":"sha256:2db00b9867bb2d867a2d2f43cce94b130291e45ac8f810aea7b6042ed818aade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/bundle.json","state_url":"https://pith.science/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/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":"2026-08-15T04:42:56Z","links":{"resolver":"https://pith.science/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ","bundle":"https://pith.science/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/bundle.json","state":"https://pith.science/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VYBYGUSYNQPS3WT4Y3UBPHSTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:7VYBYGUSYNQPS3WT4Y3UBPHSTZ","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":"24c9d34c8b13cb77502b780ff3c8bdb6b06f09bb7abb5777456b9012298fbab9","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2002-10-08T13:54:17Z","title_canon_sha256":"8bf6d0d216feb133c218dc5519d56040b0506e4347e2a5ba162a32e00ab9b6a0"},"schema_version":"1.0","source":{"id":"math/0210119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210119","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210119v1","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210119","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"7VYBYGUSYNQP","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_16","alias_value":"7VYBYGUSYNQPS3WT","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_8","alias_value":"7VYBYGUS","created_at":"2026-07-04T14:36:37Z"}],"graph_snapshots":[{"event_id":"sha256:2db00b9867bb2d867a2d2f43cce94b130291e45ac8f810aea7b6042ed818aade","target":"graph","created_at":"2026-07-04T14:36:37Z","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/math/0210119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in $\\RR^3$. This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see [CM15] for discussion of the local case and [CM13], [CM14] where we have surveyed our results about embedded minimal disks.","authors_text":"Tobias H. Colding, William P. Minicozzi II","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2002-10-08T13:54:17Z","title":"The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210119","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:d0ff3b2062dc573e22de08f241e64d565bd713f178faad6e1b3a570b54500d98","target":"record","created_at":"2026-07-04T14:36:37Z","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":"24c9d34c8b13cb77502b780ff3c8bdb6b06f09bb7abb5777456b9012298fbab9","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2002-10-08T13:54:17Z","title_canon_sha256":"8bf6d0d216feb133c218dc5519d56040b0506e4347e2a5ba162a32e00ab9b6a0"},"schema_version":"1.0","source":{"id":"math/0210119","kind":"arxiv","version":1}},"canonical_sha256":"fd701c1a92c360f96ed3e63740bcf29e5048cb93269d8fad63b73a2574d7799a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd701c1a92c360f96ed3e63740bcf29e5048cb93269d8fad63b73a2574d7799a","first_computed_at":"2026-07-04T14:36:37.159078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:37.159078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sL4Kp1F20vy3bajkUY7Og0cHpTCZK3A8TUjNKD21wyxBxj67dj1UHpDz1RweuemgkFxQOxhTFzX/88R71QgkAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:37.159490Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0210119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0ff3b2062dc573e22de08f241e64d565bd713f178faad6e1b3a570b54500d98","sha256:2db00b9867bb2d867a2d2f43cce94b130291e45ac8f810aea7b6042ed818aade"],"state_sha256":"9efdc3fc8f26584ab31212281af126816992b3398a12ace8abee9b9444261d42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlYz0Rv+fOLtqQwT4kNVk1ctgT5NvIf9NpTUM0zcUR6OsqfnyDVVSJRnPCTHS3aIqgAnTbKwQDTZ5xfRDU2pBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T04:42:56.772259Z","bundle_sha256":"f7d00cb57e912405554d8759b9826b0789ebb70a2fa20d6eebd9be75ddd19bf6"}}