{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YCENENUYC5PPKUK4CQ6DWEZ5YQ","short_pith_number":"pith:YCENENUY","canonical_record":{"source":{"id":"2404.12058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T10:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"b84cc81b435ece50e38f734651708f2789d18898a697b80bd8a1ce46e89d78b2","abstract_canon_sha256":"2038aaea1396d9e1986c4ca5131a8bbe7e230a3386d0b42e871676376b1375d8"},"schema_version":"1.0"},"canonical_sha256":"c088d23698175ef5515c143c3b133dc413b89fe340ec6ccde73d2deedf0e9403","source":{"kind":"arxiv","id":"2404.12058","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.12058","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"2404.12058v3","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.12058","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"YCENENUYC5PP","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YCENENUYC5PPKUK4","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YCENENUY","created_at":"2026-07-05T10:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YCENENUYC5PPKUK4CQ6DWEZ5YQ","target":"record","payload":{"canonical_record":{"source":{"id":"2404.12058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T10:13:35Z","cross_cats_sorted":[],"title_canon_sha256":"b84cc81b435ece50e38f734651708f2789d18898a697b80bd8a1ce46e89d78b2","abstract_canon_sha256":"2038aaea1396d9e1986c4ca5131a8bbe7e230a3386d0b42e871676376b1375d8"},"schema_version":"1.0"},"canonical_sha256":"c088d23698175ef5515c143c3b133dc413b89fe340ec6ccde73d2deedf0e9403","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:02.573063Z","signature_b64":"6kBxjON0FFdfCQbdXh1AryEfPT/UB3o5zWrDDlQAIAJyFAdYK0YG+9c2IGbzO2j0Q7ZGa649rNNID9qG+JoiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c088d23698175ef5515c143c3b133dc413b89fe340ec6ccde73d2deedf0e9403","last_reissued_at":"2026-07-05T10:26:02.572435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:02.572435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.12058","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":"2026-07-05T10:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZxKM2ejqr6rk2zrzxqeyRs9cvfe0BSolI4DWFOhwinuzl33de38gsPkl+uVQ+R2KA1DM2j9Yr+T62Q4BvluBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:56:13.016314Z"},"content_sha256":"20b0a4804d0994202405a7a73302a2ece4c8b66d9770e14e8b7192fc1b6451de","schema_version":"1.0","event_id":"sha256:20b0a4804d0994202405a7a73302a2ece4c8b66d9770e14e8b7192fc1b6451de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YCENENUYC5PPKUK4CQ6DWEZ5YQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonexistence of solutions to parabolic problems with a potential on weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia","submitted_at":"2024-04-18T10:13:35Z","abstract_excerpt":"We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exists. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12058","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.12058/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":"2026-07-05T10:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pcHNMZv6qm6YMll4DlQuRCqQIwlv8i0g5JsBvaV7+3OQ55KJ6CewuekUQhhTUev2cxMOECQWuXmoW8RGapdFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T11:56:13.016643Z"},"content_sha256":"19f498a69362fe4fb0bcc772fa46373740d55a6a65c6e21c5fd0c46796293c9a","schema_version":"1.0","event_id":"sha256:19f498a69362fe4fb0bcc772fa46373740d55a6a65c6e21c5fd0c46796293c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/bundle.json","state_url":"https://pith.science/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/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":"2026-08-19T11:56:13Z","links":{"resolver":"https://pith.science/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ","bundle":"https://pith.science/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/bundle.json","state":"https://pith.science/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCENENUYC5PPKUK4CQ6DWEZ5YQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YCENENUYC5PPKUK4CQ6DWEZ5YQ","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":"2038aaea1396d9e1986c4ca5131a8bbe7e230a3386d0b42e871676376b1375d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T10:13:35Z","title_canon_sha256":"b84cc81b435ece50e38f734651708f2789d18898a697b80bd8a1ce46e89d78b2"},"schema_version":"1.0","source":{"id":"2404.12058","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.12058","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"2404.12058v3","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.12058","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"YCENENUYC5PP","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YCENENUYC5PPKUK4","created_at":"2026-07-05T10:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YCENENUY","created_at":"2026-07-05T10:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:19f498a69362fe4fb0bcc772fa46373740d55a6a65c6e21c5fd0c46796293c9a","target":"graph","created_at":"2026-07-05T10:26:02Z","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/2404.12058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exists. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.","authors_text":"Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T10:13:35Z","title":"Nonexistence of solutions to parabolic problems with a potential on weighted graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12058","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":"sha256:20b0a4804d0994202405a7a73302a2ece4c8b66d9770e14e8b7192fc1b6451de","target":"record","created_at":"2026-07-05T10:26:02Z","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":"2038aaea1396d9e1986c4ca5131a8bbe7e230a3386d0b42e871676376b1375d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T10:13:35Z","title_canon_sha256":"b84cc81b435ece50e38f734651708f2789d18898a697b80bd8a1ce46e89d78b2"},"schema_version":"1.0","source":{"id":"2404.12058","kind":"arxiv","version":3}},"canonical_sha256":"c088d23698175ef5515c143c3b133dc413b89fe340ec6ccde73d2deedf0e9403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c088d23698175ef5515c143c3b133dc413b89fe340ec6ccde73d2deedf0e9403","first_computed_at":"2026-07-05T10:26:02.572435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:02.572435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6kBxjON0FFdfCQbdXh1AryEfPT/UB3o5zWrDDlQAIAJyFAdYK0YG+9c2IGbzO2j0Q7ZGa649rNNID9qG+JoiBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:02.573063Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.12058","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20b0a4804d0994202405a7a73302a2ece4c8b66d9770e14e8b7192fc1b6451de","sha256:19f498a69362fe4fb0bcc772fa46373740d55a6a65c6e21c5fd0c46796293c9a"],"state_sha256":"4ce61ecc2e92684f0740f586101189338de14d788b398ea4a3465a92e7680025"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VEDPnF+Qi4g1W8gd0xMiYkRDVgLBHo4H7jfvV/NIcQxkCTb0VE/b4u43pwQWicWkNckUv8Z54tXuXKtKPBMyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T11:56:13.019848Z","bundle_sha256":"9b3b935b1dd8c256293ef748aa6138ce7d961be3064f75af64fac6e524ceac86"}}