{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:L3G4YHFSQQRT3KLF3R65U5R75D","short_pith_number":"pith:L3G4YHFS","canonical_record":{"source":{"id":"1103.6229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-31T16:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"3cc209a5cc6c2766d5bbbc9876851d45c3a6abc194663a0d5faa28611daef98b","abstract_canon_sha256":"b4c4a87e123a625f8aa0765de3efc3e4f48ca277a3c595dadffa0defb38b549b"},"schema_version":"1.0"},"canonical_sha256":"5ecdcc1cb284233da965dc7dda763fe8e2badcbb5fe9243c4af34ecf56065d52","source":{"kind":"arxiv","id":"1103.6229","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6229","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6229v2","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6229","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"L3G4YHFSQQRT","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L3G4YHFSQQRT3KLF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L3G4YHFS","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:L3G4YHFSQQRT3KLF3R65U5R75D","target":"record","payload":{"canonical_record":{"source":{"id":"1103.6229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-31T16:16:58Z","cross_cats_sorted":[],"title_canon_sha256":"3cc209a5cc6c2766d5bbbc9876851d45c3a6abc194663a0d5faa28611daef98b","abstract_canon_sha256":"b4c4a87e123a625f8aa0765de3efc3e4f48ca277a3c595dadffa0defb38b549b"},"schema_version":"1.0"},"canonical_sha256":"5ecdcc1cb284233da965dc7dda763fe8e2badcbb5fe9243c4af34ecf56065d52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:23.233672Z","signature_b64":"hW+NmqPrjEC4MVLMDazO3/bOgrA6VTBH0SJhG8RXy43ULlXhZykN1MmWBclJdiAjwncwNHLxTVwAbaFmUx7JBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ecdcc1cb284233da965dc7dda763fe8e2badcbb5fe9243c4af34ecf56065d52","last_reissued_at":"2026-05-18T04:18:23.233225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:23.233225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.6229","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROINYsSlW9IMAWqMFzitk39O7UQBZ2R60ETuD2vBUfDTn1x5RwvJhEgORYbtMlTtYjbFbR20w58YsSZ/RyMMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:27.583254Z"},"content_sha256":"b133b319f83ca842f07d9c396f52819186c2d1a3bc02cefdc7a2dff08ca2a392","schema_version":"1.0","event_id":"sha256:b133b319f83ca842f07d9c396f52819186c2d1a3bc02cefdc7a2dff08ca2a392"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:L3G4YHFSQQRT3KLF3R65U5R75D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matzoh ball soup revisited: the boundary regularity issue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2011-03-31T16:16:58Z","abstract_excerpt":"We consider nonlinear diffusion equations of the form $\\partial_t u= \\Delta \\phi(u)$ in $\\mathbb R^N$ with $N \\ge 2.$ When $\\phi(s) \\equiv s$, this is just the heat equation. Let $\\Omega$ be a domain in $\\mathbb R^N$, where $\\partial\\Omega$ is bounded and $\\partial\\Omega = \\partial (\\mathbb R^N\\setminus \\bar {\\Omega})$. We consider the initial-boundary value problem, where the initial value equals zero and the boundary value equals 1, and the Cauchy problem where the initial data is the characteristic function of the set $\\Omega^c = \\mathbb R^N\\setminus \\Omega$. We settle the boundary regulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6229","kind":"arxiv","version":2},"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":"2026-05-18T04:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DhVAx14ugT+kymHAGGdAzJeey4DfnZX7aAD/KRRkRavWLXbNEbfpKFNJCiGWDMHCPWEKkmyG3RELGQE8yAQZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:27.583631Z"},"content_sha256":"9566c153dc31ef6671e32be052b46f0ba8169aa576c4d4575f24f17cabdc66eb","schema_version":"1.0","event_id":"sha256:9566c153dc31ef6671e32be052b46f0ba8169aa576c4d4575f24f17cabdc66eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3G4YHFSQQRT3KLF3R65U5R75D/bundle.json","state_url":"https://pith.science/pith/L3G4YHFSQQRT3KLF3R65U5R75D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3G4YHFSQQRT3KLF3R65U5R75D/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":"2026-06-24T08:14:27Z","links":{"resolver":"https://pith.science/pith/L3G4YHFSQQRT3KLF3R65U5R75D","bundle":"https://pith.science/pith/L3G4YHFSQQRT3KLF3R65U5R75D/bundle.json","state":"https://pith.science/pith/L3G4YHFSQQRT3KLF3R65U5R75D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3G4YHFSQQRT3KLF3R65U5R75D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L3G4YHFSQQRT3KLF3R65U5R75D","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":"b4c4a87e123a625f8aa0765de3efc3e4f48ca277a3c595dadffa0defb38b549b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-31T16:16:58Z","title_canon_sha256":"3cc209a5cc6c2766d5bbbc9876851d45c3a6abc194663a0d5faa28611daef98b"},"schema_version":"1.0","source":{"id":"1103.6229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6229","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6229v2","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6229","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"L3G4YHFSQQRT","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L3G4YHFSQQRT3KLF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L3G4YHFS","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:9566c153dc31ef6671e32be052b46f0ba8169aa576c4d4575f24f17cabdc66eb","target":"graph","created_at":"2026-05-18T04:18:23Z","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 consider nonlinear diffusion equations of the form $\\partial_t u= \\Delta \\phi(u)$ in $\\mathbb R^N$ with $N \\ge 2.$ When $\\phi(s) \\equiv s$, this is just the heat equation. Let $\\Omega$ be a domain in $\\mathbb R^N$, where $\\partial\\Omega$ is bounded and $\\partial\\Omega = \\partial (\\mathbb R^N\\setminus \\bar {\\Omega})$. We consider the initial-boundary value problem, where the initial value equals zero and the boundary value equals 1, and the Cauchy problem where the initial data is the characteristic function of the set $\\Omega^c = \\mathbb R^N\\setminus \\Omega$. We settle the boundary regulari","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-31T16:16:58Z","title":"Matzoh ball soup revisited: the boundary regularity issue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6229","kind":"arxiv","version":2},"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:b133b319f83ca842f07d9c396f52819186c2d1a3bc02cefdc7a2dff08ca2a392","target":"record","created_at":"2026-05-18T04:18:23Z","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":"b4c4a87e123a625f8aa0765de3efc3e4f48ca277a3c595dadffa0defb38b549b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-31T16:16:58Z","title_canon_sha256":"3cc209a5cc6c2766d5bbbc9876851d45c3a6abc194663a0d5faa28611daef98b"},"schema_version":"1.0","source":{"id":"1103.6229","kind":"arxiv","version":2}},"canonical_sha256":"5ecdcc1cb284233da965dc7dda763fe8e2badcbb5fe9243c4af34ecf56065d52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ecdcc1cb284233da965dc7dda763fe8e2badcbb5fe9243c4af34ecf56065d52","first_computed_at":"2026-05-18T04:18:23.233225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:23.233225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hW+NmqPrjEC4MVLMDazO3/bOgrA6VTBH0SJhG8RXy43ULlXhZykN1MmWBclJdiAjwncwNHLxTVwAbaFmUx7JBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:23.233672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.6229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b133b319f83ca842f07d9c396f52819186c2d1a3bc02cefdc7a2dff08ca2a392","sha256:9566c153dc31ef6671e32be052b46f0ba8169aa576c4d4575f24f17cabdc66eb"],"state_sha256":"25ae4f389a73d1d3c876eca5a51df5c84e103153603c040ffddc61a063bce3ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JJH+450YhINJlin7CDMSXRJCiCA+iNQvuMdn76YLmdjK+r3ex0C/wsJKJPg3ZBmlBNrSIvbTJtu88uzkNOPDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:14:27.585604Z","bundle_sha256":"c7c84716a7b4a81303d177a46f3f21f0b4ea21d68000d64cea032095a3b26b95"}}