{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D5QEV62MWQABZ2MVFAHMKSNUSM","short_pith_number":"pith:D5QEV62M","canonical_record":{"source":{"id":"1002.0999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T13:55:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9172e2773e1648a758b0f7d75554b694fd711adde12b44bd0f65a8a567a9a636","abstract_canon_sha256":"880282235d87be8418a09be3424eca21e98ee979525977ae075d780d4e0528dc"},"schema_version":"1.0"},"canonical_sha256":"1f604afb4cb4001ce995280ec549b4930532e866f8f5a53dac1ce32ea00e5c73","source":{"kind":"arxiv","id":"1002.0999","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0999","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0999v1","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0999","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"D5QEV62MWQAB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5QEV62MWQABZ2MV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5QEV62M","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D5QEV62MWQABZ2MVFAHMKSNUSM","target":"record","payload":{"canonical_record":{"source":{"id":"1002.0999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T13:55:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"9172e2773e1648a758b0f7d75554b694fd711adde12b44bd0f65a8a567a9a636","abstract_canon_sha256":"880282235d87be8418a09be3424eca21e98ee979525977ae075d780d4e0528dc"},"schema_version":"1.0"},"canonical_sha256":"1f604afb4cb4001ce995280ec549b4930532e866f8f5a53dac1ce32ea00e5c73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:24.217214Z","signature_b64":"+QKgwXIZjAu5kRivkzLQJn2rqvf4lHQRvreoNFSiqkAg4owsOkH4xtyTyXSOF469diZETWk90zlxpHfL7I50Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f604afb4cb4001ce995280ec549b4930532e866f8f5a53dac1ce32ea00e5c73","last_reissued_at":"2026-05-18T04:42:24.216803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:24.216803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.0999","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":"2026-05-18T04:42:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jH1mNKXJevXCt3Ye4oLDGEcFyGoxGWK4BU5MGbq0RtCNfgb6JG920w8+K5vkvd+nL7hkI7iPBREry+G2KbNjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:25:31.812866Z"},"content_sha256":"7b912bbc94552dc603f2b99e0d4fa704adfd51c739f05c729a8b20782044011f","schema_version":"1.0","event_id":"sha256:7b912bbc94552dc603f2b99e0d4fa704adfd51c739f05c729a8b20782044011f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D5QEV62MWQABZ2MVFAHMKSNUSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heat conduction: a telegraph-type model with self-similar behavior of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Imre Ferenc Barna, Robert Kersner","submitted_at":"2010-02-04T13:55:08Z","abstract_excerpt":"For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \\frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\\epsilon S_{tt} + \\frac{a}{t} S_t = S_{xx}$ . This model already has a typical self-similar solution which may be written as product of two travelling waves modulo a time-dependent factor and might play a role of intermediate asymptotics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0999","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":""},"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":"2026-05-18T04:42:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nl3Yhp0e3++2LQ1wVs0KOJ0EWnpeyl0b5H0BPeLOaOuSen0m+RLAxmT14A634Z8kMk/Bc+52DNOgEn6Zj76UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:25:31.813203Z"},"content_sha256":"b15a437924ceb1fe15637d838a380fd8d97314d8fe4471d7dffef97ec977c7c0","schema_version":"1.0","event_id":"sha256:b15a437924ceb1fe15637d838a380fd8d97314d8fe4471d7dffef97ec977c7c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/bundle.json","state_url":"https://pith.science/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/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":"2026-07-02T09:25:31Z","links":{"resolver":"https://pith.science/pith/D5QEV62MWQABZ2MVFAHMKSNUSM","bundle":"https://pith.science/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/bundle.json","state":"https://pith.science/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5QEV62MWQABZ2MVFAHMKSNUSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D5QEV62MWQABZ2MVFAHMKSNUSM","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":"880282235d87be8418a09be3424eca21e98ee979525977ae075d780d4e0528dc","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T13:55:08Z","title_canon_sha256":"9172e2773e1648a758b0f7d75554b694fd711adde12b44bd0f65a8a567a9a636"},"schema_version":"1.0","source":{"id":"1002.0999","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0999","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0999v1","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0999","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"D5QEV62MWQAB","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5QEV62MWQABZ2MV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5QEV62M","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:b15a437924ceb1fe15637d838a380fd8d97314d8fe4471d7dffef97ec977c7c0","target":"graph","created_at":"2026-05-18T04:42:24Z","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":"For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \\frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\\epsilon S_{tt} + \\frac{a}{t} S_t = S_{xx}$ . This model already has a typical self-similar solution which may be written as product of two travelling waves modulo a time-dependent factor and might play a role of intermediate asymptotics.","authors_text":"Imre Ferenc Barna, Robert Kersner","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T13:55:08Z","title":"Heat conduction: a telegraph-type model with self-similar behavior of solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0999","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":"sha256:7b912bbc94552dc603f2b99e0d4fa704adfd51c739f05c729a8b20782044011f","target":"record","created_at":"2026-05-18T04:42:24Z","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":"880282235d87be8418a09be3424eca21e98ee979525977ae075d780d4e0528dc","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-04T13:55:08Z","title_canon_sha256":"9172e2773e1648a758b0f7d75554b694fd711adde12b44bd0f65a8a567a9a636"},"schema_version":"1.0","source":{"id":"1002.0999","kind":"arxiv","version":1}},"canonical_sha256":"1f604afb4cb4001ce995280ec549b4930532e866f8f5a53dac1ce32ea00e5c73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f604afb4cb4001ce995280ec549b4930532e866f8f5a53dac1ce32ea00e5c73","first_computed_at":"2026-05-18T04:42:24.216803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:24.216803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+QKgwXIZjAu5kRivkzLQJn2rqvf4lHQRvreoNFSiqkAg4owsOkH4xtyTyXSOF469diZETWk90zlxpHfL7I50Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:24.217214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0999","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b912bbc94552dc603f2b99e0d4fa704adfd51c739f05c729a8b20782044011f","sha256:b15a437924ceb1fe15637d838a380fd8d97314d8fe4471d7dffef97ec977c7c0"],"state_sha256":"b3b0f8f05c0eb029aa5cf258ce2e3d1a45527e7d43693ee4fdf8193b26dd5f2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glKvoJ7/4tv4WeU5GRyWLXnsoGt3aRiDCUhqX3fBlSAyVpxMy5+sosp/Om6HKHS1u3rWDZQuFSFWhyRyu+WsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T09:25:31.815120Z","bundle_sha256":"41a1f9a290078ef1fde40176f52656d48bd8235ddae36ccbe20f68f0802fb3ca"}}