{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QFOQHR5B6PY2GBNHC3KQZW5ING","short_pith_number":"pith:QFOQHR5B","canonical_record":{"source":{"id":"1509.01189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T16:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"c56962d319783c9a35977583cd5aa48f13099f62d8a3ab846132b71fa218ed86","abstract_canon_sha256":"9b322601f7c0e64537a0ee9c72ca82b4ab57430b6879740bd45e86c99a9150b5"},"schema_version":"1.0"},"canonical_sha256":"815d03c7a1f3f1a305a716d50cdba869be46eae223a53f98bd58389527edbcff","source":{"kind":"arxiv","id":"1509.01189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01189","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01189v1","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01189","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"QFOQHR5B6PY2","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFOQHR5B6PY2GBNH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFOQHR5B","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QFOQHR5B6PY2GBNHC3KQZW5ING","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T16:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"c56962d319783c9a35977583cd5aa48f13099f62d8a3ab846132b71fa218ed86","abstract_canon_sha256":"9b322601f7c0e64537a0ee9c72ca82b4ab57430b6879740bd45e86c99a9150b5"},"schema_version":"1.0"},"canonical_sha256":"815d03c7a1f3f1a305a716d50cdba869be46eae223a53f98bd58389527edbcff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:59.356175Z","signature_b64":"u+bOqtnmwU9hQXOseh+3ke/L9oB7l4Tx8HG/7dYmKsmqgaYEQ4fW+81bWFgb4im6+ZPPKrqo6RWzJHmj8jLOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"815d03c7a1f3f1a305a716d50cdba869be46eae223a53f98bd58389527edbcff","last_reissued_at":"2026-05-18T01:33:59.355671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:59.355671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01189","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":"2026-05-18T01:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5PfQRZSEo5jWclDs8bFRGTXwHigD/OongP/eggzL4lYONCEzSUnXjIu0R/cseXhr/s7UoN6OSBsdcuqdK6aCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:53:50.748476Z"},"content_sha256":"5dc18ad7689e6f438b06befab5f96119c903a0d695ce11b8f77b567a921d804c","schema_version":"1.0","event_id":"sha256:5dc18ad7689e6f438b06befab5f96119c903a0d695ce11b8f77b567a921d804c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QFOQHR5B6PY2GBNHC3KQZW5ING","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolation inequalities in pattern formation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eleonora Cinti, Felix Otto","submitted_at":"2015-09-02T16:54:06Z","abstract_excerpt":"We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in the study of branching in superconductors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01189","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":"2026-05-18T01:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYMqkJGwNP0YrTJ5EhSLQeCdGJnPPZlK+WKTgWnrdQEd60iidvoClhFuNLRbuadV7TUK4UPLI8F5gLcr03UeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:53:50.748816Z"},"content_sha256":"2bcada1f5c1fd6bd087a0caae91419473a1d550666487661e2355bbe877192d8","schema_version":"1.0","event_id":"sha256:2bcada1f5c1fd6bd087a0caae91419473a1d550666487661e2355bbe877192d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/bundle.json","state_url":"https://pith.science/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/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":"2026-06-01T08:53:50Z","links":{"resolver":"https://pith.science/pith/QFOQHR5B6PY2GBNHC3KQZW5ING","bundle":"https://pith.science/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/bundle.json","state":"https://pith.science/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFOQHR5B6PY2GBNHC3KQZW5ING/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QFOQHR5B6PY2GBNHC3KQZW5ING","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":"9b322601f7c0e64537a0ee9c72ca82b4ab57430b6879740bd45e86c99a9150b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T16:54:06Z","title_canon_sha256":"c56962d319783c9a35977583cd5aa48f13099f62d8a3ab846132b71fa218ed86"},"schema_version":"1.0","source":{"id":"1509.01189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01189","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01189v1","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01189","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"QFOQHR5B6PY2","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFOQHR5B6PY2GBNH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFOQHR5B","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:2bcada1f5c1fd6bd087a0caae91419473a1d550666487661e2355bbe877192d8","target":"graph","created_at":"2026-05-18T01:33:59Z","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":"We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in the study of branching in superconductors.","authors_text":"Eleonora Cinti, Felix Otto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T16:54:06Z","title":"Interpolation inequalities in pattern formation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01189","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":"sha256:5dc18ad7689e6f438b06befab5f96119c903a0d695ce11b8f77b567a921d804c","target":"record","created_at":"2026-05-18T01:33:59Z","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":"9b322601f7c0e64537a0ee9c72ca82b4ab57430b6879740bd45e86c99a9150b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T16:54:06Z","title_canon_sha256":"c56962d319783c9a35977583cd5aa48f13099f62d8a3ab846132b71fa218ed86"},"schema_version":"1.0","source":{"id":"1509.01189","kind":"arxiv","version":1}},"canonical_sha256":"815d03c7a1f3f1a305a716d50cdba869be46eae223a53f98bd58389527edbcff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"815d03c7a1f3f1a305a716d50cdba869be46eae223a53f98bd58389527edbcff","first_computed_at":"2026-05-18T01:33:59.355671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:59.355671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u+bOqtnmwU9hQXOseh+3ke/L9oB7l4Tx8HG/7dYmKsmqgaYEQ4fW+81bWFgb4im6+ZPPKrqo6RWzJHmj8jLOCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:59.356175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dc18ad7689e6f438b06befab5f96119c903a0d695ce11b8f77b567a921d804c","sha256:2bcada1f5c1fd6bd087a0caae91419473a1d550666487661e2355bbe877192d8"],"state_sha256":"5665b5731e65cf831048714f6893a581ee30680c76e876b8e4522af64a961431"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GCZPm+4hzBevipONV7h/99oth6qmEUptA4iZ2+ktAWQ2XJIj21Yy18w5Ocnp6ZKgQx+9dPE6CFenr1w3b4V4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:53:50.751228Z","bundle_sha256":"a1f2f3695a656188500348ea06f66d61e3a94cb8d2eb355a5ae9c94e71bf7dec"}}