{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LA2YQNSJNWCJ4ROLAKT3FP7B4O","short_pith_number":"pith:LA2YQNSJ","canonical_record":{"source":{"id":"1401.1175","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-06T19:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"f4666ceda4507fc8e4099204259d4b5fcad85ec0f5f52efa22914955d3bbd45b","abstract_canon_sha256":"106a40da080a95710a21d969690c5d1785373b41c0d5b2805cae0bcc8c22aeac"},"schema_version":"1.0"},"canonical_sha256":"58358836496d849e45cb02a7b2bfe1e395a294685e7dcf718b24e1284ee70dcb","source":{"kind":"arxiv","id":"1401.1175","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1175","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1175v3","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1175","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"LA2YQNSJNWCJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LA2YQNSJNWCJ4ROL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LA2YQNSJ","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LA2YQNSJNWCJ4ROLAKT3FP7B4O","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1175","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-06T19:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"f4666ceda4507fc8e4099204259d4b5fcad85ec0f5f52efa22914955d3bbd45b","abstract_canon_sha256":"106a40da080a95710a21d969690c5d1785373b41c0d5b2805cae0bcc8c22aeac"},"schema_version":"1.0"},"canonical_sha256":"58358836496d849e45cb02a7b2bfe1e395a294685e7dcf718b24e1284ee70dcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:26.063945Z","signature_b64":"dx9MiAEATWJYlowX4ZEOzwQMpZdDgjZvlDCruBNJetoTkQHMCF2Ic3+BuUQ4MYmwRIh+wnVvEmL+dW3FG9gPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58358836496d849e45cb02a7b2bfe1e395a294685e7dcf718b24e1284ee70dcb","last_reissued_at":"2026-05-18T02:52:26.063405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:26.063405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1175","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xXsnYFVOtFOwIlSUbJm16dIygCC6WQTjCoC7yd2EW/vnIRJGLbsD9oQjevun9WWuSRrIqprMi4NEy4w9QWdWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:00:03.515934Z"},"content_sha256":"e06a5936a50dc528c727cc04ed4b9df2100ac1ee612d2e08eb7b6c8c81772f9c","schema_version":"1.0","event_id":"sha256:e06a5936a50dc528c727cc04ed4b9df2100ac1ee612d2e08eb7b6c8c81772f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LA2YQNSJNWCJ4ROLAKT3FP7B4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation of Reactions in Inhomogeneous Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrej Zlatos","submitted_at":"2014-01-06T19:46:10Z","abstract_excerpt":"Consider reaction-diffusion equation $u_t=\\Delta u + f(x,u)$ with $x\\in\\mathbb{R}^d$ and general inhomogeneous ignition reaction $f\\ge 0$ vanishing at $u=0,1$. Typical solutions $0\\le u\\le 1$ transition from $0$ to $1$ as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on $f$ we show that in dimensions $d\\le 3$, the Hausdorff distance of the super-level sets $\\{u\\ge\\epsilon\\}$ and $\\{u\\ge 1-\\epsilon\\}$ remains uniformly bounded in time for each $\\epsilon\\in(0,1)$. Thus, $u$ remains uniformly in time close to the charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1175","kind":"arxiv","version":3},"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":"2026-05-18T02:52:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1hLa+cJffdvixRr5BXOZeD1DlnTkOj1N2nh5sdtYHtHiuuxhEevpj7MzqF8qSB/pG2wCg9jFafmRII5iJixBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:00:03.516277Z"},"content_sha256":"76179e16b101bc454b183a2426e45a4d72766ca920f9f9257ff1e9294ce0ec42","schema_version":"1.0","event_id":"sha256:76179e16b101bc454b183a2426e45a4d72766ca920f9f9257ff1e9294ce0ec42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/bundle.json","state_url":"https://pith.science/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/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":"2026-06-02T21:00:03Z","links":{"resolver":"https://pith.science/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O","bundle":"https://pith.science/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/bundle.json","state":"https://pith.science/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LA2YQNSJNWCJ4ROLAKT3FP7B4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LA2YQNSJNWCJ4ROLAKT3FP7B4O","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":"106a40da080a95710a21d969690c5d1785373b41c0d5b2805cae0bcc8c22aeac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-06T19:46:10Z","title_canon_sha256":"f4666ceda4507fc8e4099204259d4b5fcad85ec0f5f52efa22914955d3bbd45b"},"schema_version":"1.0","source":{"id":"1401.1175","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1175","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1175v3","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1175","created_at":"2026-05-18T02:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"LA2YQNSJNWCJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LA2YQNSJNWCJ4ROL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LA2YQNSJ","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:76179e16b101bc454b183a2426e45a4d72766ca920f9f9257ff1e9294ce0ec42","target":"graph","created_at":"2026-05-18T02:52:26Z","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"},"paper":{"abstract_excerpt":"Consider reaction-diffusion equation $u_t=\\Delta u + f(x,u)$ with $x\\in\\mathbb{R}^d$ and general inhomogeneous ignition reaction $f\\ge 0$ vanishing at $u=0,1$. Typical solutions $0\\le u\\le 1$ transition from $0$ to $1$ as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on $f$ we show that in dimensions $d\\le 3$, the Hausdorff distance of the super-level sets $\\{u\\ge\\epsilon\\}$ and $\\{u\\ge 1-\\epsilon\\}$ remains uniformly bounded in time for each $\\epsilon\\in(0,1)$. Thus, $u$ remains uniformly in time close to the charact","authors_text":"Andrej Zlatos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-06T19:46:10Z","title":"Propagation of Reactions in Inhomogeneous Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1175","kind":"arxiv","version":3},"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:e06a5936a50dc528c727cc04ed4b9df2100ac1ee612d2e08eb7b6c8c81772f9c","target":"record","created_at":"2026-05-18T02:52:26Z","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":"106a40da080a95710a21d969690c5d1785373b41c0d5b2805cae0bcc8c22aeac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-06T19:46:10Z","title_canon_sha256":"f4666ceda4507fc8e4099204259d4b5fcad85ec0f5f52efa22914955d3bbd45b"},"schema_version":"1.0","source":{"id":"1401.1175","kind":"arxiv","version":3}},"canonical_sha256":"58358836496d849e45cb02a7b2bfe1e395a294685e7dcf718b24e1284ee70dcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58358836496d849e45cb02a7b2bfe1e395a294685e7dcf718b24e1284ee70dcb","first_computed_at":"2026-05-18T02:52:26.063405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:26.063405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dx9MiAEATWJYlowX4ZEOzwQMpZdDgjZvlDCruBNJetoTkQHMCF2Ic3+BuUQ4MYmwRIh+wnVvEmL+dW3FG9gPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:26.063945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1175","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e06a5936a50dc528c727cc04ed4b9df2100ac1ee612d2e08eb7b6c8c81772f9c","sha256:76179e16b101bc454b183a2426e45a4d72766ca920f9f9257ff1e9294ce0ec42"],"state_sha256":"53fcb6c1990193993dfe00a2ad891c38204eb1924548e973f617c1515b00525c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s6JPQCp/J9ProIrhmlroeep64BcRCVEFGop8XeL5nI2ILTX+RThw2Lr7k4Mqjy6v1cYUIg36nods2Qb3e3zNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:00:03.518214Z","bundle_sha256":"9dd23486c04fb565ad0b79385ce41c883ad38d385139cd13abb0ab14c37a85f4"}}