{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:6AANQPFAZFVV3FHG4HA63AL66Y","short_pith_number":"pith:6AANQPFA","canonical_record":{"source":{"id":"2208.14522","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-08-30T20:13:13Z","cross_cats_sorted":["cs.NA","math.CV","math.NA"],"title_canon_sha256":"d8ad0a597f6959e1a8bf1cbbaa50d498a8ce6c6bbcbde5c48d597a676e979c9e","abstract_canon_sha256":"9f82596f5619b07568389e939bcd04ee208b1407022f9a300ba3a897330efde6"},"schema_version":"1.0"},"canonical_sha256":"f000d83ca0c96b5d94e6e1c1ed817ef6291368ab32bd1e59c96c50d414e741c3","source":{"kind":"arxiv","id":"2208.14522","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14522","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14522v1","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14522","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"6AANQPFAZFVV","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"6AANQPFAZFVV3FHG","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"6AANQPFA","created_at":"2026-07-05T05:43:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:6AANQPFAZFVV3FHG4HA63AL66Y","target":"record","payload":{"canonical_record":{"source":{"id":"2208.14522","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-08-30T20:13:13Z","cross_cats_sorted":["cs.NA","math.CV","math.NA"],"title_canon_sha256":"d8ad0a597f6959e1a8bf1cbbaa50d498a8ce6c6bbcbde5c48d597a676e979c9e","abstract_canon_sha256":"9f82596f5619b07568389e939bcd04ee208b1407022f9a300ba3a897330efde6"},"schema_version":"1.0"},"canonical_sha256":"f000d83ca0c96b5d94e6e1c1ed817ef6291368ab32bd1e59c96c50d414e741c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:43:54.348037Z","signature_b64":"/QVyTl4/9m1DqH3GKNBJ4QuT4B5+64qQa1xjXETocZtgIeM5ZF25uk2o5wR1O91PJ1B+rARQhcvNCkU59oElCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f000d83ca0c96b5d94e6e1c1ed817ef6291368ab32bd1e59c96c50d414e741c3","last_reissued_at":"2026-07-05T05:43:54.347620Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:43:54.347620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.14522","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":"2026-07-05T05:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUzgQkFd5AMnxubdFEIdQqmkj4/Tfr67vqy61+cKBMv217wkQJVWADyFbhVmj/LsDBztHhf0pv5uZdPLtL25DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:42:49.247627Z"},"content_sha256":"252f5b5f4bd352a1a01e7e8041290a653ff8bb1f20072be36aee788249a3a367","schema_version":"1.0","event_id":"sha256:252f5b5f4bd352a1a01e7e8041290a653ff8bb1f20072be36aee788249a3a367"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:6AANQPFAZFVV3FHG4HA63AL66Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow up in a periodic semilinear heat equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.CV","math.NA"],"primary_cat":"math.AP","authors_text":"J.A.C. Weideman, John R. King, Marco Fasondini","submitted_at":"2022-08-30T20:13:13Z","abstract_excerpt":"Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel results include various asymptotic approximations that are, in combination, valid over the entire space and time interval right up to and including the blow-up time. Preliminary results on continuing a numerical solution beyond the singularity are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14522","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/2208.14522/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":"2026-07-05T05:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZccjrqX+1YuCe/EwJPCDXVtfnFPCu87rLvH5HZ812bgA4qxEkq4gQ0cqg+NXFcceu+LyIELX1cfdCGQABDi+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:42:49.248035Z"},"content_sha256":"208f8b89cc769efc4ad0a721c5687f01fb27c0ebb7fd5edfc9fd2af9d6373cd4","schema_version":"1.0","event_id":"sha256:208f8b89cc769efc4ad0a721c5687f01fb27c0ebb7fd5edfc9fd2af9d6373cd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6AANQPFAZFVV3FHG4HA63AL66Y/bundle.json","state_url":"https://pith.science/pith/6AANQPFAZFVV3FHG4HA63AL66Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6AANQPFAZFVV3FHG4HA63AL66Y/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":"2026-07-05T14:42:49Z","links":{"resolver":"https://pith.science/pith/6AANQPFAZFVV3FHG4HA63AL66Y","bundle":"https://pith.science/pith/6AANQPFAZFVV3FHG4HA63AL66Y/bundle.json","state":"https://pith.science/pith/6AANQPFAZFVV3FHG4HA63AL66Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6AANQPFAZFVV3FHG4HA63AL66Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6AANQPFAZFVV3FHG4HA63AL66Y","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":"9f82596f5619b07568389e939bcd04ee208b1407022f9a300ba3a897330efde6","cross_cats_sorted":["cs.NA","math.CV","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-08-30T20:13:13Z","title_canon_sha256":"d8ad0a597f6959e1a8bf1cbbaa50d498a8ce6c6bbcbde5c48d597a676e979c9e"},"schema_version":"1.0","source":{"id":"2208.14522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14522","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14522v1","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14522","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"6AANQPFAZFVV","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"6AANQPFAZFVV3FHG","created_at":"2026-07-05T05:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"6AANQPFA","created_at":"2026-07-05T05:43:54Z"}],"graph_snapshots":[{"event_id":"sha256:208f8b89cc769efc4ad0a721c5687f01fb27c0ebb7fd5edfc9fd2af9d6373cd4","target":"graph","created_at":"2026-07-05T05:43:54Z","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/2208.14522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and starting out from a nearly flat, positive initial condition. Novel results include various asymptotic approximations that are, in combination, valid over the entire space and time interval right up to and including the blow-up time. Preliminary results on continuing a numerical solution beyond the singularity are also presented.","authors_text":"J.A.C. Weideman, John R. King, Marco Fasondini","cross_cats":["cs.NA","math.CV","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-08-30T20:13:13Z","title":"Blow up in a periodic semilinear heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14522","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":"sha256:252f5b5f4bd352a1a01e7e8041290a653ff8bb1f20072be36aee788249a3a367","target":"record","created_at":"2026-07-05T05:43:54Z","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":"9f82596f5619b07568389e939bcd04ee208b1407022f9a300ba3a897330efde6","cross_cats_sorted":["cs.NA","math.CV","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-08-30T20:13:13Z","title_canon_sha256":"d8ad0a597f6959e1a8bf1cbbaa50d498a8ce6c6bbcbde5c48d597a676e979c9e"},"schema_version":"1.0","source":{"id":"2208.14522","kind":"arxiv","version":1}},"canonical_sha256":"f000d83ca0c96b5d94e6e1c1ed817ef6291368ab32bd1e59c96c50d414e741c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f000d83ca0c96b5d94e6e1c1ed817ef6291368ab32bd1e59c96c50d414e741c3","first_computed_at":"2026-07-05T05:43:54.347620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:43:54.347620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/QVyTl4/9m1DqH3GKNBJ4QuT4B5+64qQa1xjXETocZtgIeM5ZF25uk2o5wR1O91PJ1B+rARQhcvNCkU59oElCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:43:54.348037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.14522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:252f5b5f4bd352a1a01e7e8041290a653ff8bb1f20072be36aee788249a3a367","sha256:208f8b89cc769efc4ad0a721c5687f01fb27c0ebb7fd5edfc9fd2af9d6373cd4"],"state_sha256":"1ca31a6fae65ff849a673dc4235180b02eefb9813ab0956c7135420390dfc5d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXS0t/CTUYTe48LSALcxFaIHuQwvM3KymmypC8d90ejBfv+21e0TYBRRYBmt3xpUj5E/R/wHWyPhvuB3pU8CBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T14:42:49.250200Z","bundle_sha256":"16d0243017dfc409624d92068578113950ceaef07755bff527df246463b57f8b"}}