{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:T3ON6RSS2KT6PYUOKVS3MYTNDV","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":"c063802482fc91f6282b28e3bd026730edc03ef7519aaa15e21de254e9c8de64","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-06T19:27:55Z","title_canon_sha256":"00e1fe37c81be61f1b59a13c3f6a5950b5b33248fa4daff228534f8da116c968"},"schema_version":"1.0","source":{"id":"math/0702156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702156","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702156v2","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702156","created_at":"2026-05-18T04:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"T3ON6RSS2KT6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"T3ON6RSS2KT6PYUO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"T3ON6RSS","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:526ed9d916b57c590af035cf507c0f8ae8fc841826b6c7bebb3bc19bf63c5f94","target":"graph","created_at":"2026-05-18T04:32:00Z","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":"We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\\Delta u = u^p$ with $p\\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.","authors_text":"A. Wasserman, D. Maison, P. Bizon","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-02-06T19:27:55Z","title":"Self-similar solutions of semilinear wave equations with a focusing nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702156","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":"sha256:7e4310bd3ff5b92bec63952a4e1e2f08240b8dc0edfc1b5f76326c6801123cb5","target":"record","created_at":"2026-05-18T04:32:00Z","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":"c063802482fc91f6282b28e3bd026730edc03ef7519aaa15e21de254e9c8de64","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-06T19:27:55Z","title_canon_sha256":"00e1fe37c81be61f1b59a13c3f6a5950b5b33248fa4daff228534f8da116c968"},"schema_version":"1.0","source":{"id":"math/0702156","kind":"arxiv","version":2}},"canonical_sha256":"9edcdf4652d2a7e7e28e5565b6626d1d59d07be63ebab4d4d1a3694478575f2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9edcdf4652d2a7e7e28e5565b6626d1d59d07be63ebab4d4d1a3694478575f2e","first_computed_at":"2026-05-18T04:32:00.173775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:00.173775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rPEVZ9VWUK2+eYtM+aN8YCrQnm1Cf4+nuqp++xCH1Mq1X09OLlcozttqv9HG8YEWFhtwbdZ4DpO3hK0VutG+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:00.174454Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e4310bd3ff5b92bec63952a4e1e2f08240b8dc0edfc1b5f76326c6801123cb5","sha256:526ed9d916b57c590af035cf507c0f8ae8fc841826b6c7bebb3bc19bf63c5f94"],"state_sha256":"af2ae92e662d103836fc4025041267f6b134bbd4636da35b68a31d82abac830b"}