{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:P7L6EIGKELN7GJUX4GMA7FI4V7","short_pith_number":"pith:P7L6EIGK","canonical_record":{"source":{"id":"1604.04192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-14T15:45:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"923b772fb7d797becf62e2436778f818478cd4e0dfb49f26054658f39bb8a356","abstract_canon_sha256":"afef6dfc675de4db38dc2df95b4bd227c2fe035e55549c80cfd03813ebfeb8b6"},"schema_version":"1.0"},"canonical_sha256":"7fd7e220ca22dbf32697e1980f951cafdb5cba18e57ae6648aeb2044694e37f4","source":{"kind":"arxiv","id":"1604.04192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04192","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04192v1","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04192","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"P7L6EIGKELN7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7L6EIGKELN7GJUX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7L6EIGK","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:P7L6EIGKELN7GJUX4GMA7FI4V7","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-14T15:45:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"923b772fb7d797becf62e2436778f818478cd4e0dfb49f26054658f39bb8a356","abstract_canon_sha256":"afef6dfc675de4db38dc2df95b4bd227c2fe035e55549c80cfd03813ebfeb8b6"},"schema_version":"1.0"},"canonical_sha256":"7fd7e220ca22dbf32697e1980f951cafdb5cba18e57ae6648aeb2044694e37f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:14.824884Z","signature_b64":"cQd0VBG4J/eu4GfZGOOG/vrt6ivQBx9ZKa32bjR+uwiXWIbzTJH6iEiEc23n3cTGSgYQ22rcIzxMNJPZ0/5oBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd7e220ca22dbf32697e1980f951cafdb5cba18e57ae6648aeb2044694e37f4","last_reissued_at":"2026-05-18T00:05:14.824234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:14.824234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04192","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":"2026-05-18T00:05:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3dsT/hzrX0c/30Vp9qmftCjAt5/XbkS/UL2eMPGifaRoDdvimGgNfK99CCLZKM1fe/Yty9iuJ2ZXchQf8BU0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:57:14.233556Z"},"content_sha256":"b1fbc95688d44b22a0be3bca689138697aa32bd16132dcb164525082e9ab7c02","schema_version":"1.0","event_id":"sha256:b1fbc95688d44b22a0be3bca689138697aa32bd16132dcb164525082e9ab7c02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:P7L6EIGKELN7GJUX4GMA7FI4V7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Surgery, Dynamics and Applications To Natural Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Sofia Lambropoulou, Stathis Antoniou","submitted_at":"2016-04-14T15:45:54Z","abstract_excerpt":"In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To do this, we first present a schematic model which extends the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on surfaces but are three-dimensional, we fill the interior space by defining the notion of solid 2-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04192","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":"2026-05-18T00:05:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzBb/nAPG78pu53+NxQHxfSg1KMwna61G4QW157cuSXXUApMQx6bUMXgEjERqey8BetrFNmFEhf7ilKoWKYtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:57:14.234182Z"},"content_sha256":"5fa301a92860a0fe1d2d9e6af05834ddb78258f64234efcc43fdef2ddab7f9ca","schema_version":"1.0","event_id":"sha256:5fa301a92860a0fe1d2d9e6af05834ddb78258f64234efcc43fdef2ddab7f9ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/bundle.json","state_url":"https://pith.science/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/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":"2026-05-31T03:57:14Z","links":{"resolver":"https://pith.science/pith/P7L6EIGKELN7GJUX4GMA7FI4V7","bundle":"https://pith.science/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/bundle.json","state":"https://pith.science/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7L6EIGKELN7GJUX4GMA7FI4V7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P7L6EIGKELN7GJUX4GMA7FI4V7","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":"afef6dfc675de4db38dc2df95b4bd227c2fe035e55549c80cfd03813ebfeb8b6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-14T15:45:54Z","title_canon_sha256":"923b772fb7d797becf62e2436778f818478cd4e0dfb49f26054658f39bb8a356"},"schema_version":"1.0","source":{"id":"1604.04192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04192","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04192v1","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04192","created_at":"2026-05-18T00:05:14Z"},{"alias_kind":"pith_short_12","alias_value":"P7L6EIGKELN7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7L6EIGKELN7GJUX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7L6EIGK","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:5fa301a92860a0fe1d2d9e6af05834ddb78258f64234efcc43fdef2ddab7f9ca","target":"graph","created_at":"2026-05-18T00:05:14Z","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":"In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To do this, we first present a schematic model which extends the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on surfaces but are three-dimensional, we fill the interior space by defining the notion of solid 2-dime","authors_text":"Sofia Lambropoulou, Stathis Antoniou","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-14T15:45:54Z","title":"Topological Surgery, Dynamics and Applications To Natural Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04192","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:b1fbc95688d44b22a0be3bca689138697aa32bd16132dcb164525082e9ab7c02","target":"record","created_at":"2026-05-18T00:05:14Z","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":"afef6dfc675de4db38dc2df95b4bd227c2fe035e55549c80cfd03813ebfeb8b6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-14T15:45:54Z","title_canon_sha256":"923b772fb7d797becf62e2436778f818478cd4e0dfb49f26054658f39bb8a356"},"schema_version":"1.0","source":{"id":"1604.04192","kind":"arxiv","version":1}},"canonical_sha256":"7fd7e220ca22dbf32697e1980f951cafdb5cba18e57ae6648aeb2044694e37f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fd7e220ca22dbf32697e1980f951cafdb5cba18e57ae6648aeb2044694e37f4","first_computed_at":"2026-05-18T00:05:14.824234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:14.824234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQd0VBG4J/eu4GfZGOOG/vrt6ivQBx9ZKa32bjR+uwiXWIbzTJH6iEiEc23n3cTGSgYQ22rcIzxMNJPZ0/5oBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:14.824884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1fbc95688d44b22a0be3bca689138697aa32bd16132dcb164525082e9ab7c02","sha256:5fa301a92860a0fe1d2d9e6af05834ddb78258f64234efcc43fdef2ddab7f9ca"],"state_sha256":"d1b56b276bbaa0abaff597be2ec35d5bc86a28f783dc9eedd7dfb1894216b05a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zq8YJXxuFTXJBKrueazo82S3ztFv2ieKVs3EcCdER6p5WJ1wjyc8JOm7jxfogQEwRXrd7rUATvtglIVq3KNTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:57:14.237450Z","bundle_sha256":"7c000987d211fe5e9cf8f630919ffcd5e03d00139d533e9314806408ec125bd8"}}