{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:D4M3HJBYUBKQLDQBKXZX2WUN4O","short_pith_number":"pith:D4M3HJBY","canonical_record":{"source":{"id":"1811.12357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T18:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"1cbf00c76d3b0882a38c50cdb2cb1799ae44bb1d422b3a67b9ae40c0f9c483c7","abstract_canon_sha256":"b4e1531e197ec78753953a1fa9647d6e9d4e524682e0e7438dac9317d082bf2f"},"schema_version":"1.0"},"canonical_sha256":"1f19b3a438a055058e0155f37d5a8de3aacb87655db009627dbba388a9159e21","source":{"kind":"arxiv","id":"1811.12357","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12357","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12357v2","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12357","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"D4M3HJBYUBKQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4M3HJBYUBKQLDQB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4M3HJBY","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:D4M3HJBYUBKQLDQBKXZX2WUN4O","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T18:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"1cbf00c76d3b0882a38c50cdb2cb1799ae44bb1d422b3a67b9ae40c0f9c483c7","abstract_canon_sha256":"b4e1531e197ec78753953a1fa9647d6e9d4e524682e0e7438dac9317d082bf2f"},"schema_version":"1.0"},"canonical_sha256":"1f19b3a438a055058e0155f37d5a8de3aacb87655db009627dbba388a9159e21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:47.149614Z","signature_b64":"xjAZGzpeFuZcoYn4XyRTh6hX7iksnFwCrv3UCqhm6bjv4suI5t9xJbwH7WE6Z5bBUfFCieKNrZyd/SnMieg3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f19b3a438a055058e0155f37d5a8de3aacb87655db009627dbba388a9159e21","last_reissued_at":"2026-05-17T23:58:47.149209Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:47.149209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12357","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"98QtRVA+n7M7r747MY7OimouSPDu1Uv89piLEuwC0VRDd1MoOfKfrDX7523fjti/hp6x94+42bl9Vb4mbL6WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:26:47.854562Z"},"content_sha256":"b5bcf322b54f3689ad6baee69b77fe9a7649320b19992764f96009e07efd4e82","schema_version":"1.0","event_id":"sha256:b5bcf322b54f3689ad6baee69b77fe9a7649320b19992764f96009e07efd4e82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:D4M3HJBYUBKQLDQBKXZX2WUN4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strichartz estimates without loss outside many strictly convex obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Lafontaine","submitted_at":"2018-11-29T18:09:12Z","abstract_excerpt":"We prove Strichartz estimates without loss for the Schr\\\"odinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending the approach we introduced previously for the two convex case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12357","kind":"arxiv","version":2},"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":"2026-05-17T23:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"67P/6CaSlSzN+RshgfedrYK4Boj0hr2QRzZ2NGD2YxbZmJkotaCIcZre9aT3Id5hjv/kVtzu3zYjLW3VYsH+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:26:47.854901Z"},"content_sha256":"90a9c21974b9b0297173f4f108396891e7dc5b3e1317ed411de7af9dab0067ff","schema_version":"1.0","event_id":"sha256:90a9c21974b9b0297173f4f108396891e7dc5b3e1317ed411de7af9dab0067ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/bundle.json","state_url":"https://pith.science/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/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":"2026-07-06T12:26:47Z","links":{"resolver":"https://pith.science/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O","bundle":"https://pith.science/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/bundle.json","state":"https://pith.science/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4M3HJBYUBKQLDQBKXZX2WUN4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D4M3HJBYUBKQLDQBKXZX2WUN4O","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":"b4e1531e197ec78753953a1fa9647d6e9d4e524682e0e7438dac9317d082bf2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T18:09:12Z","title_canon_sha256":"1cbf00c76d3b0882a38c50cdb2cb1799ae44bb1d422b3a67b9ae40c0f9c483c7"},"schema_version":"1.0","source":{"id":"1811.12357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12357","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12357v2","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12357","created_at":"2026-05-17T23:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"D4M3HJBYUBKQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4M3HJBYUBKQLDQB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4M3HJBY","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:90a9c21974b9b0297173f4f108396891e7dc5b3e1317ed411de7af9dab0067ff","target":"graph","created_at":"2026-05-17T23:58:47Z","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 Strichartz estimates without loss for the Schr\\\"odinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending the approach we introduced previously for the two convex case.","authors_text":"David Lafontaine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T18:09:12Z","title":"Strichartz estimates without loss outside many strictly convex obstacles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12357","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:b5bcf322b54f3689ad6baee69b77fe9a7649320b19992764f96009e07efd4e82","target":"record","created_at":"2026-05-17T23:58:47Z","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":"b4e1531e197ec78753953a1fa9647d6e9d4e524682e0e7438dac9317d082bf2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T18:09:12Z","title_canon_sha256":"1cbf00c76d3b0882a38c50cdb2cb1799ae44bb1d422b3a67b9ae40c0f9c483c7"},"schema_version":"1.0","source":{"id":"1811.12357","kind":"arxiv","version":2}},"canonical_sha256":"1f19b3a438a055058e0155f37d5a8de3aacb87655db009627dbba388a9159e21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f19b3a438a055058e0155f37d5a8de3aacb87655db009627dbba388a9159e21","first_computed_at":"2026-05-17T23:58:47.149209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:47.149209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjAZGzpeFuZcoYn4XyRTh6hX7iksnFwCrv3UCqhm6bjv4suI5t9xJbwH7WE6Z5bBUfFCieKNrZyd/SnMieg3Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:47.149614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5bcf322b54f3689ad6baee69b77fe9a7649320b19992764f96009e07efd4e82","sha256:90a9c21974b9b0297173f4f108396891e7dc5b3e1317ed411de7af9dab0067ff"],"state_sha256":"77c6c374e0cab443ad2f03f094588b8a637f574a53a3fb93fd571ea7b16e1bfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7b7fsi10KXiWt704id1NWUfTLOwvDPgyQdeEj6IpZTDgFdvdi87d5a7Cqpkr7qONrOob5UJpBONgNc4PFYQCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T12:26:47.856742Z","bundle_sha256":"3c3520d4ecb807418c1b00b87bc430177d8eee3a2b946c1346be33e39456b5d2"}}