{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:B4IMMN3JGD4B4PL3VANAHGDFND","short_pith_number":"pith:B4IMMN3J","schema_version":"1.0","canonical_sha256":"0f10c6376930f81e3d7ba81a03986568ca223e64e54e6a1cce30365534d53d27","source":{"kind":"arxiv","id":"2608.13531","version":1},"attestation_state":"computed","paper":{"title":"Non-uniqueness of Brakke flows starting from minimal surfaces with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kotaro Motegi","submitted_at":"2026-08-13T17:48:51Z","abstract_excerpt":"We prove the existence of a genuinely time-dependent Brakke flow starting from $\\Gamma_0 \\subset \\mathbb{R}^{n+1}$ whose associated multiplicity-one varifold is stationary, provided that, at some singular point, the scale-invariant $L^2$ distance of $\\Gamma_0$ from an $n$-dimensional plane has sufficiently small limsup as the scale tends to zero. This yields the dynamical instability of $\\Gamma_0$, a notion recently introduced by Stuvard and Tonegawa, and hence the non-uniqueness of Brakke flows starting from $\\Gamma_0$. A notable feature of our result is that it holds without assuming the uni"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.13531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T17:48:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e30623dd8eac7fe2daab18def73bd26467a1960b1ae2e796c51875abc1aaec0a","abstract_canon_sha256":"81e490bcd8294df28017186c2d02537c694ffbe9f5dee0669be3d1f3af8c6ad7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:24:58.588660Z","signature_b64":"GSmNK0yuk0wQ7Xh7CRqP90X16bZRhA2hPyhkEKwhnpnB6Jp+NzR9JaovnbuyzjvllNobvn6nZAduPVRblRJfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f10c6376930f81e3d7ba81a03986568ca223e64e54e6a1cce30365534d53d27","last_reissued_at":"2026-08-14T01:24:58.586355Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:24:58.586355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-uniqueness of Brakke flows starting from minimal surfaces with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kotaro Motegi","submitted_at":"2026-08-13T17:48:51Z","abstract_excerpt":"We prove the existence of a genuinely time-dependent Brakke flow starting from $\\Gamma_0 \\subset \\mathbb{R}^{n+1}$ whose associated multiplicity-one varifold is stationary, provided that, at some singular point, the scale-invariant $L^2$ distance of $\\Gamma_0$ from an $n$-dimensional plane has sufficiently small limsup as the scale tends to zero. This yields the dynamical instability of $\\Gamma_0$, a notion recently introduced by Stuvard and Tonegawa, and hence the non-uniqueness of Brakke flows starting from $\\Gamma_0$. A notable feature of our result is that it holds without assuming the uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13531","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/2608.13531/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.13531","created_at":"2026-08-14T01:24:58.587921+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.13531v1","created_at":"2026-08-14T01:24:58.587921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13531","created_at":"2026-08-14T01:24:58.587921+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4IMMN3JGD4B","created_at":"2026-08-14T01:24:58.587921+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4IMMN3JGD4B4PL3","created_at":"2026-08-14T01:24:58.587921+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4IMMN3J","created_at":"2026-08-14T01:24:58.587921+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND","json":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND.json","graph_json":"https://pith.science/api/pith-number/B4IMMN3JGD4B4PL3VANAHGDFND/graph.json","events_json":"https://pith.science/api/pith-number/B4IMMN3JGD4B4PL3VANAHGDFND/events.json","paper":"https://pith.science/paper/B4IMMN3J"},"agent_actions":{"view_html":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND","download_json":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND.json","view_paper":"https://pith.science/paper/B4IMMN3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.13531&json=true","fetch_graph":"https://pith.science/api/pith-number/B4IMMN3JGD4B4PL3VANAHGDFND/graph.json","fetch_events":"https://pith.science/api/pith-number/B4IMMN3JGD4B4PL3VANAHGDFND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND/action/storage_attestation","attest_author":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND/action/author_attestation","sign_citation":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND/action/citation_signature","submit_replication":"https://pith.science/pith/B4IMMN3JGD4B4PL3VANAHGDFND/action/replication_record"}},"created_at":"2026-08-14T01:24:58.587921+00:00","updated_at":"2026-08-14T01:24:58.587921+00:00"}