{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:T4B5RD4AMAM2UFIBVCIPX5S56P","short_pith_number":"pith:T4B5RD4A","canonical_record":{"source":{"id":"1012.5861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-29T02:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"b26db4f05211068e550ee162023c519b8639842aa26918214c4425a34ae7d293","abstract_canon_sha256":"ce9fd2cde2c2263583ef9f031f2773d7144e433c1dea42361e609da6cf2e5620"},"schema_version":"1.0"},"canonical_sha256":"9f03d88f806019aa1501a890fbf65df3e60977b0485eda2c10a969019c841cde","source":{"kind":"arxiv","id":"1012.5861","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5861","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5861v1","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5861","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"T4B5RD4AMAM2","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T4B5RD4AMAM2UFIB","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T4B5RD4A","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:T4B5RD4AMAM2UFIBVCIPX5S56P","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-29T02:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"b26db4f05211068e550ee162023c519b8639842aa26918214c4425a34ae7d293","abstract_canon_sha256":"ce9fd2cde2c2263583ef9f031f2773d7144e433c1dea42361e609da6cf2e5620"},"schema_version":"1.0"},"canonical_sha256":"9f03d88f806019aa1501a890fbf65df3e60977b0485eda2c10a969019c841cde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:21.322507Z","signature_b64":"y4mcdjLFPaOlkPRucrYUDUb5GhBZJyV/ZMHsmZjJW2hQjEZaaK/diG8EHXqoXm0la6qIZoaGFcHYehfhwi81Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f03d88f806019aa1501a890fbf65df3e60977b0485eda2c10a969019c841cde","last_reissued_at":"2026-05-18T04:32:21.321721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:21.321721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5861","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":"2026-05-18T04:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxWB+f9BK9VQRSyT6bSybAYogqevgYOBFVsNaCqhAfAbHQhRBXg1cE29720vI8Jd3C0r4jnkdXyOIEGWsEN6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:32:23.764014Z"},"content_sha256":"bfe40bf0c896a39d6eddbf5acb3442dd1abdd220b8f0376d6b5ff88798fe784c","schema_version":"1.0","event_id":"sha256:bfe40bf0c896a39d6eddbf5acb3442dd1abdd220b8f0376d6b5ff88798fe784c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:T4B5RD4AMAM2UFIBVCIPX5S56P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary value problem for a classical semilinear parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Ma","submitted_at":"2010-12-29T02:42:26Z","abstract_excerpt":"In this paper, we study the boundary value problem of the classical semilinear parabolic equations $$ u_t-\\Delta u=|u|^{p-1}u, \\ \\ in \\ \\ \\Omega\\times (0,T) $$ and $u=0$ on the boundary $\\partial\\Omega\\times [0,T)$ and $u=\\phi$ at $t=0$, where $\\Omega\\subset R^n$ is a compact $C^1$ domain, $1<p\\leq p_S$ is a fixed constant, and $\\phi\\in C^2_0(\\Omega)$ is a given smooth function. Introducing new idea, we show that there are two sets $\\tilde{W}$ and $\\tilde{Z}$ such that for $\\phi\\in W$, there is a global positive solution $u(t)\\in \\tilde{W}$ with $h^1$ omega limit $\\{0\\}$ and for $\\phi\\in \\tild"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5861","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":"2026-05-18T04:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g6J7ghczFZjwfKgjnimylmiatlQ4iFuEfzXTD4MEiucZ0/Kon07Ad1+4mvwtKc1A0ArCsTbhc0TM0kdUhiDPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:32:23.764368Z"},"content_sha256":"56fe5faaab9c8e2e644de98342271855f4a2d3acd9e15f595f02838195c4a7fc","schema_version":"1.0","event_id":"sha256:56fe5faaab9c8e2e644de98342271855f4a2d3acd9e15f595f02838195c4a7fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/bundle.json","state_url":"https://pith.science/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/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":"2026-06-01T14:32:23Z","links":{"resolver":"https://pith.science/pith/T4B5RD4AMAM2UFIBVCIPX5S56P","bundle":"https://pith.science/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/bundle.json","state":"https://pith.science/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4B5RD4AMAM2UFIBVCIPX5S56P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T4B5RD4AMAM2UFIBVCIPX5S56P","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":"ce9fd2cde2c2263583ef9f031f2773d7144e433c1dea42361e609da6cf2e5620","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-29T02:42:26Z","title_canon_sha256":"b26db4f05211068e550ee162023c519b8639842aa26918214c4425a34ae7d293"},"schema_version":"1.0","source":{"id":"1012.5861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5861","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5861v1","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5861","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"T4B5RD4AMAM2","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T4B5RD4AMAM2UFIB","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T4B5RD4A","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:56fe5faaab9c8e2e644de98342271855f4a2d3acd9e15f595f02838195c4a7fc","target":"graph","created_at":"2026-05-18T04:32:21Z","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":"In this paper, we study the boundary value problem of the classical semilinear parabolic equations $$ u_t-\\Delta u=|u|^{p-1}u, \\ \\ in \\ \\ \\Omega\\times (0,T) $$ and $u=0$ on the boundary $\\partial\\Omega\\times [0,T)$ and $u=\\phi$ at $t=0$, where $\\Omega\\subset R^n$ is a compact $C^1$ domain, $1<p\\leq p_S$ is a fixed constant, and $\\phi\\in C^2_0(\\Omega)$ is a given smooth function. Introducing new idea, we show that there are two sets $\\tilde{W}$ and $\\tilde{Z}$ such that for $\\phi\\in W$, there is a global positive solution $u(t)\\in \\tilde{W}$ with $h^1$ omega limit $\\{0\\}$ and for $\\phi\\in \\tild","authors_text":"Li Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-29T02:42:26Z","title":"Boundary value problem for a classical semilinear parabolic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5861","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:bfe40bf0c896a39d6eddbf5acb3442dd1abdd220b8f0376d6b5ff88798fe784c","target":"record","created_at":"2026-05-18T04:32:21Z","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":"ce9fd2cde2c2263583ef9f031f2773d7144e433c1dea42361e609da6cf2e5620","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-29T02:42:26Z","title_canon_sha256":"b26db4f05211068e550ee162023c519b8639842aa26918214c4425a34ae7d293"},"schema_version":"1.0","source":{"id":"1012.5861","kind":"arxiv","version":1}},"canonical_sha256":"9f03d88f806019aa1501a890fbf65df3e60977b0485eda2c10a969019c841cde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f03d88f806019aa1501a890fbf65df3e60977b0485eda2c10a969019c841cde","first_computed_at":"2026-05-18T04:32:21.321721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:21.321721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y4mcdjLFPaOlkPRucrYUDUb5GhBZJyV/ZMHsmZjJW2hQjEZaaK/diG8EHXqoXm0la6qIZoaGFcHYehfhwi81Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:21.322507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfe40bf0c896a39d6eddbf5acb3442dd1abdd220b8f0376d6b5ff88798fe784c","sha256:56fe5faaab9c8e2e644de98342271855f4a2d3acd9e15f595f02838195c4a7fc"],"state_sha256":"d424bbc19767dfcc99c08a6b7258ddb5411d0f7249bb38396eacd7260be937d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cHgOQoZw4dZGX+k2CBTb8U++YABfYdAQ4lX2N010X7mqcgx+K5Cb8f8KlBw7bzwFfoPdDaC5ecFNxJVSLU+jCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:32:23.766219Z","bundle_sha256":"b7b98f9c042ad3761da5e665cfe8438cb49f9c636e853b57be128574340d62e3"}}