{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EOKH2NF4WW4UHVZRHPGKGH6EYZ","short_pith_number":"pith:EOKH2NF4","canonical_record":{"source":{"id":"2403.09876","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e849932ff435f88200636d3d9af7d2d8d0884214c669ef96feaebce4d4fa01b4","abstract_canon_sha256":"2df61f3b66f957a69d11d87c42e107d73dc41a214b619b0a11c024b382d0eb22"},"schema_version":"1.0"},"canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","source":{"kind":"arxiv","id":"2403.09876","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.09876","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"2403.09876v1","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.09876","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"EOKH2NF4WW4U","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_16","alias_value":"EOKH2NF4WW4UHVZR","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_8","alias_value":"EOKH2NF4","created_at":"2026-07-05T07:56:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EOKH2NF4WW4UHVZRHPGKGH6EYZ","target":"record","payload":{"canonical_record":{"source":{"id":"2403.09876","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e849932ff435f88200636d3d9af7d2d8d0884214c669ef96feaebce4d4fa01b4","abstract_canon_sha256":"2df61f3b66f957a69d11d87c42e107d73dc41a214b619b0a11c024b382d0eb22"},"schema_version":"1.0"},"canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:56:26.773438Z","signature_b64":"TV4qa2vro6oJ42pCm9SxTMXkOkDPKXJx06rwOFrYLfR8VkuIWreuAZqZ5P5ufRkOyQ0jNnYGqZPDY8FPTXKKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","last_reissued_at":"2026-07-05T07:56:26.773054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:56:26.773054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.09876","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":"2026-07-05T07:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UP2Dx4BiQ9iRPBhoc3zS8n1cNBrTXTtx4vPJsPLT3dqtYlEqioveuzDipEMqMrfVrXo+4NRFwpmbeUzm0HPXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:12:23.735998Z"},"content_sha256":"c9cca5c65936c14506beec7a680625b5a1643e9d7b3cc69752f3995f1e69de15","schema_version":"1.0","event_id":"sha256:c9cca5c65936c14506beec7a680625b5a1643e9d7b3cc69752f3995f1e69de15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EOKH2NF4WW4UHVZRHPGKGH6EYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Which shapes can appear in a Curve Shortening Flow Singularity?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alex Moon, Aris Lemmenes, Edgar Gevorgyan, Ellie DeCleene, Evan Patrick Davis, Paige Ellingson, Sigurd Angenent, Tyler Joseph Tommasi, Yamin Zhou, Ziheng Feng","submitted_at":"2024-03-14T21:13:38Z","abstract_excerpt":"We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's Figure-Eight curve, and we conjecture a generalization of the Coiculescu-Schwarz asymptotic bow-tie "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09876","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/2403.09876/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":"2026-07-05T07:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bClKLBsxj8MVNfmEwXR1lwXm4jnXUkLh3UIXaG0O/hFgzWm6p3cc4F8r9q76OJ1jfexcTVTV1jVjBkiQFZ3XBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:12:23.736521Z"},"content_sha256":"ea6ad3691c7c53283a0bc35979ffc4a71e2e90985ffd55d0d4e60ea4cc7189e9","schema_version":"1.0","event_id":"sha256:ea6ad3691c7c53283a0bc35979ffc4a71e2e90985ffd55d0d4e60ea4cc7189e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/bundle.json","state_url":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/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":"2026-08-06T02:12:23Z","links":{"resolver":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ","bundle":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/bundle.json","state":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EOKH2NF4WW4UHVZRHPGKGH6EYZ","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":"2df61f3b66f957a69d11d87c42e107d73dc41a214b619b0a11c024b382d0eb22","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","title_canon_sha256":"e849932ff435f88200636d3d9af7d2d8d0884214c669ef96feaebce4d4fa01b4"},"schema_version":"1.0","source":{"id":"2403.09876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.09876","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"2403.09876v1","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.09876","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"EOKH2NF4WW4U","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_16","alias_value":"EOKH2NF4WW4UHVZR","created_at":"2026-07-05T07:56:26Z"},{"alias_kind":"pith_short_8","alias_value":"EOKH2NF4","created_at":"2026-07-05T07:56:26Z"}],"graph_snapshots":[{"event_id":"sha256:ea6ad3691c7c53283a0bc35979ffc4a71e2e90985ffd55d0d4e60ea4cc7189e9","target":"graph","created_at":"2026-07-05T07:56:26Z","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/2403.09876/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's Figure-Eight curve, and we conjecture a generalization of the Coiculescu-Schwarz asymptotic bow-tie ","authors_text":"Alex Moon, Aris Lemmenes, Edgar Gevorgyan, Ellie DeCleene, Evan Patrick Davis, Paige Ellingson, Sigurd Angenent, Tyler Joseph Tommasi, Yamin Zhou, Ziheng Feng","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","title":"Which shapes can appear in a Curve Shortening Flow Singularity?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09876","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:c9cca5c65936c14506beec7a680625b5a1643e9d7b3cc69752f3995f1e69de15","target":"record","created_at":"2026-07-05T07:56:26Z","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":"2df61f3b66f957a69d11d87c42e107d73dc41a214b619b0a11c024b382d0eb22","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","title_canon_sha256":"e849932ff435f88200636d3d9af7d2d8d0884214c669ef96feaebce4d4fa01b4"},"schema_version":"1.0","source":{"id":"2403.09876","kind":"arxiv","version":1}},"canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","first_computed_at":"2026-07-05T07:56:26.773054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:56:26.773054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TV4qa2vro6oJ42pCm9SxTMXkOkDPKXJx06rwOFrYLfR8VkuIWreuAZqZ5P5ufRkOyQ0jNnYGqZPDY8FPTXKKDw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:56:26.773438Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.09876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9cca5c65936c14506beec7a680625b5a1643e9d7b3cc69752f3995f1e69de15","sha256:ea6ad3691c7c53283a0bc35979ffc4a71e2e90985ffd55d0d4e60ea4cc7189e9"],"state_sha256":"d779f308cf606ec05eb0be14318e1649f708d8420380ebc728a852584e7b9571"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/y0vduUHj4dMLKCX+4YOwFWiSyoJKnDhWM6Mk0/m4urjMfVEWdkP0iIq0oxoXXCB9gBh57DRxM4+6euK4DOqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T02:12:23.741490Z","bundle_sha256":"0f7f7b2a164cee33dddc4b20090300a185122af1ab170ed02baaae9cb3f01f3f"}}