{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NOMPFB36IXVU5NCT54HHRFZKOJ","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":"ac3ab1a05c1e9e839d4d24ca93d339eafccfab6c13a19eac2763f2ce034c1b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-21T11:39:55Z","title_canon_sha256":"749dd2f177a869217b1da9513e62e817372c6d4388f198c8cce634e54bffc3be"},"schema_version":"1.0","source":{"id":"2406.15069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.15069","created_at":"2026-07-05T08:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"2406.15069v2","created_at":"2026-07-05T08:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.15069","created_at":"2026-07-05T08:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"NOMPFB36IXVU","created_at":"2026-07-05T08:41:04Z"},{"alias_kind":"pith_short_16","alias_value":"NOMPFB36IXVU5NCT","created_at":"2026-07-05T08:41:04Z"},{"alias_kind":"pith_short_8","alias_value":"NOMPFB36","created_at":"2026-07-05T08:41:04Z"}],"graph_snapshots":[{"event_id":"sha256:d9197b2e721443fc2683649f629e784f3aa26f0bccad87b90d333fe50317157f","target":"graph","created_at":"2026-07-05T08:41:04Z","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/2406.15069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the Laplace operator $\\lambda_1(G)$ on the graph is positive. According to an interaction between the behavior of $f$ close to $0$ and the value $\\lambda_1(G)$, we get the existence of a global in time solution or blow-up of any nonnegative solution, provided that the initial datum is nontrivial.","authors_text":"Fabio Punzo, Gabriele Grillo, Giulia Meglioli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-21T11:39:55Z","title":"Blow-up and global existence for semilinear parabolic equations on infinite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15069","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":"sha256:45a9b045e15c51580865f651550e0d1aaeb83964bb648be05abc9f42bcf09014","target":"record","created_at":"2026-07-05T08:41:04Z","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":"ac3ab1a05c1e9e839d4d24ca93d339eafccfab6c13a19eac2763f2ce034c1b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-06-21T11:39:55Z","title_canon_sha256":"749dd2f177a869217b1da9513e62e817372c6d4388f198c8cce634e54bffc3be"},"schema_version":"1.0","source":{"id":"2406.15069","kind":"arxiv","version":2}},"canonical_sha256":"6b98f2877e45eb4eb453ef0e78972a726bc674d03877f99dbf77290cb2c88c5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b98f2877e45eb4eb453ef0e78972a726bc674d03877f99dbf77290cb2c88c5a","first_computed_at":"2026-07-05T08:41:04.349102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:41:04.349102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTKDvvNQLsOvYIFwu8ATJnW7+Puj4jcTvuViWlKt3HuM1UmOI98imm9WaKwNftxYxZPrha254T4FdPluSpAbAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:41:04.349578Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.15069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45a9b045e15c51580865f651550e0d1aaeb83964bb648be05abc9f42bcf09014","sha256:d9197b2e721443fc2683649f629e784f3aa26f0bccad87b90d333fe50317157f"],"state_sha256":"71a005888a3e20d66e8c160302cf5f11ec25ad1ab556fc9462cd65fba4bbb502"}