{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:T7H2PNS3C47O6BYS4GBJ3XHE4V","short_pith_number":"pith:T7H2PNS3","canonical_record":{"source":{"id":"math/0702698","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-02-23T12:52:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"364046a6226488c1eed7169c4acbd37cd791d23ad0af990daaea0236228fe9c2","abstract_canon_sha256":"718c98b117062c710a931089a0e9f0c8f4e1654c81422b41775d20435397fcf6"},"schema_version":"1.0"},"canonical_sha256":"9fcfa7b65b173eef0712e1829ddce4e5527aa1837e42556b0f141da862c64204","source":{"kind":"arxiv","id":"math/0702698","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702698","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702698v1","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702698","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"T7H2PNS3C47O","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_16","alias_value":"T7H2PNS3C47O6BYS","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_8","alias_value":"T7H2PNS3","created_at":"2026-07-04T14:59:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:T7H2PNS3C47O6BYS4GBJ3XHE4V","target":"record","payload":{"canonical_record":{"source":{"id":"math/0702698","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-02-23T12:52:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"364046a6226488c1eed7169c4acbd37cd791d23ad0af990daaea0236228fe9c2","abstract_canon_sha256":"718c98b117062c710a931089a0e9f0c8f4e1654c81422b41775d20435397fcf6"},"schema_version":"1.0"},"canonical_sha256":"9fcfa7b65b173eef0712e1829ddce4e5527aa1837e42556b0f141da862c64204","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:59:42.094662Z","signature_b64":"JjrB578zs20ZJ+HUiD1j/p34tWqdtGZz8FyTPwZYbCTJK9m38lMktXBaMNHkV8dh/8alaGj2PB8/nqqRVI0wCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fcfa7b65b173eef0712e1829ddce4e5527aa1837e42556b0f141da862c64204","last_reissued_at":"2026-07-04T14:59:42.094309Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:59:42.094309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0702698","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":"2026-07-04T14:59:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1IAN2LQRsJ9GCPy5N7zBmuADbSf3JbHCaHkaQnD9TVpuBkeOU+QpJQ8RP0oQoFsQJO4qebpZMG7s85HVPhu3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:28:34.127097Z"},"content_sha256":"5e1c59fa9ac3b386d8fdabf46f9d6eaaefb570a06779a1b77457abfb543d7d07","schema_version":"1.0","event_id":"sha256:5e1c59fa9ac3b386d8fdabf46f9d6eaaefb570a06779a1b77457abfb543d7d07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:T7H2PNS3C47O6BYS4GBJ3XHE4V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-similarly expanding networks to curve shortening flow","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Felix Schulze, Oliver C. Schn\\\"urer","submitted_at":"2007-02-23T12:52:48Z","abstract_excerpt":"We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702698","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/0702698/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":"2026-07-04T14:59:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vR9F+kT30sok0qI58hPO6h0SCJJQa61wFwl22xWCu3cpiw2Hk6tk/fhuJlBuWCDlBj7Ilqb7REmzAk4mmwAUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:28:34.127998Z"},"content_sha256":"2931702e3a01b546ad7ba9ee0a1122ba142e9e84059ca7d0beb85c0e709246f0","schema_version":"1.0","event_id":"sha256:2931702e3a01b546ad7ba9ee0a1122ba142e9e84059ca7d0beb85c0e709246f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/bundle.json","state_url":"https://pith.science/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/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":"2026-08-17T03:28:34Z","links":{"resolver":"https://pith.science/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V","bundle":"https://pith.science/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/bundle.json","state":"https://pith.science/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7H2PNS3C47O6BYS4GBJ3XHE4V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:T7H2PNS3C47O6BYS4GBJ3XHE4V","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":"718c98b117062c710a931089a0e9f0c8f4e1654c81422b41775d20435397fcf6","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.DG","submitted_at":"2007-02-23T12:52:48Z","title_canon_sha256":"364046a6226488c1eed7169c4acbd37cd791d23ad0af990daaea0236228fe9c2"},"schema_version":"1.0","source":{"id":"math/0702698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702698","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702698v1","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702698","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"T7H2PNS3C47O","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_16","alias_value":"T7H2PNS3C47O6BYS","created_at":"2026-07-04T14:59:42Z"},{"alias_kind":"pith_short_8","alias_value":"T7H2PNS3","created_at":"2026-07-04T14:59:42Z"}],"graph_snapshots":[{"event_id":"sha256:2931702e3a01b546ad7ba9ee0a1122ba142e9e84059ca7d0beb85c0e709246f0","target":"graph","created_at":"2026-07-04T14:59:42Z","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/0702698/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.","authors_text":"Felix Schulze, Oliver C. Schn\\\"urer","cross_cats":["math.AP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-02-23T12:52:48Z","title":"Self-similarly expanding networks to curve shortening flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702698","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":"sha256:5e1c59fa9ac3b386d8fdabf46f9d6eaaefb570a06779a1b77457abfb543d7d07","target":"record","created_at":"2026-07-04T14:59:42Z","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":"718c98b117062c710a931089a0e9f0c8f4e1654c81422b41775d20435397fcf6","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.DG","submitted_at":"2007-02-23T12:52:48Z","title_canon_sha256":"364046a6226488c1eed7169c4acbd37cd791d23ad0af990daaea0236228fe9c2"},"schema_version":"1.0","source":{"id":"math/0702698","kind":"arxiv","version":1}},"canonical_sha256":"9fcfa7b65b173eef0712e1829ddce4e5527aa1837e42556b0f141da862c64204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fcfa7b65b173eef0712e1829ddce4e5527aa1837e42556b0f141da862c64204","first_computed_at":"2026-07-04T14:59:42.094309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:59:42.094309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JjrB578zs20ZJ+HUiD1j/p34tWqdtGZz8FyTPwZYbCTJK9m38lMktXBaMNHkV8dh/8alaGj2PB8/nqqRVI0wCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:59:42.094662Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e1c59fa9ac3b386d8fdabf46f9d6eaaefb570a06779a1b77457abfb543d7d07","sha256:2931702e3a01b546ad7ba9ee0a1122ba142e9e84059ca7d0beb85c0e709246f0"],"state_sha256":"bb155548c2a76cd66c85057f56701bd0700549f8402a265db1a0b78787dd8eab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5i98ewP8ybrJKVPU0LtCx1uGTYZE5ghoMUCii8bkTY687RMYNHuNO2yNpOXOM/pyNHiZkGI4KC+B4v/kotCcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T03:28:34.133248Z","bundle_sha256":"d708d8479cb0934174058e789e0d2203e5e9c3559ee273b9eb230f383a42f94e"}}