{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2KTPISX6ZDLRFEWOQEZVBKLYF7","short_pith_number":"pith:2KTPISX6","canonical_record":{"source":{"id":"1407.6276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T15:52:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9ed5242e734ab3dabfb68351ad2c0618888635dcb78ca38c9eb7fb7dc30efe5c","abstract_canon_sha256":"673ee461abec12cf699fbb0e6e3adf027c93954902dc91f8d83de049a484a904"},"schema_version":"1.0"},"canonical_sha256":"d2a6f44afec8d71292ce813350a9782fe464445f81c443d7e34fd274f4842e7d","source":{"kind":"arxiv","id":"1407.6276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6276","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6276v1","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6276","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"2KTPISX6ZDLR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KTPISX6ZDLRFEWO","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KTPISX6","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2KTPISX6ZDLRFEWOQEZVBKLYF7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T15:52:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9ed5242e734ab3dabfb68351ad2c0618888635dcb78ca38c9eb7fb7dc30efe5c","abstract_canon_sha256":"673ee461abec12cf699fbb0e6e3adf027c93954902dc91f8d83de049a484a904"},"schema_version":"1.0"},"canonical_sha256":"d2a6f44afec8d71292ce813350a9782fe464445f81c443d7e34fd274f4842e7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:00.615492Z","signature_b64":"PYin6dHGAtR/XFFK014eofL45iEPrZfh/4Fd5QbWARX1IM9mc4fsrts68K1H8gURAzdJL0RRaqhnHp5Zpf93Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a6f44afec8d71292ce813350a9782fe464445f81c443d7e34fd274f4842e7d","last_reissued_at":"2026-05-18T01:19:00.614962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:00.614962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6276","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":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mj+iPj4IvqCA+86737iYx7BGeJeJgP9zNVNaxwOWuRtdRCfvArqh0dps85d9+iysmG4XU7C/NLv/YIkyBJ54AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:41:37.720256Z"},"content_sha256":"dcb93651ccfb914ee45bcaddb76a7ae8d472d2fbcae1583bee60eeebd4cb9d73","schema_version":"1.0","event_id":"sha256:dcb93651ccfb914ee45bcaddb76a7ae8d472d2fbcae1583bee60eeebd4cb9d73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2KTPISX6ZDLRFEWOQEZVBKLYF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gustav Holzegel, Jared Speck, Sergiu Klainerman, Willie Wong","submitted_at":"2014-07-23T15:52:28Z","abstract_excerpt":"In his 2007 monograph, D. Christodoulou proved a remarkable result giving a detailed description of shock formation, for small $H^s$-initial conditions ($s$ sufficiently large), in solutions to the relativistic Euler equations in three space dimensions. His work provided a significant advancement over a large body of prior work concerning the long-time behavior of solutions to higher-dimensional quasilinear wave equations, initiated by F. John in the mid 1970's and continued by S. Klainerman, T. Sideris, L. H\\\"ormander, H. Lindblad, S. Alinhac, and others. Our goal in this paper is to give an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6276","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":"2026-05-18T01:19:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkgljYHXebHmyYJK+pQ+cfgXd05IFGHj+NxR9bJKKUAJR2V6AdgT9f9dHn/a+g6rZ5XFgVYUOKLqAlbQYw5YCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:41:37.720997Z"},"content_sha256":"e47210041409f6a1178bb882b3c006c6e21c8d44f08a372807347b034e0f6559","schema_version":"1.0","event_id":"sha256:e47210041409f6a1178bb882b3c006c6e21c8d44f08a372807347b034e0f6559"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/bundle.json","state_url":"https://pith.science/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/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":"2026-05-26T19:41:37Z","links":{"resolver":"https://pith.science/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7","bundle":"https://pith.science/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/bundle.json","state":"https://pith.science/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KTPISX6ZDLRFEWOQEZVBKLYF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2KTPISX6ZDLRFEWOQEZVBKLYF7","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":"673ee461abec12cf699fbb0e6e3adf027c93954902dc91f8d83de049a484a904","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T15:52:28Z","title_canon_sha256":"9ed5242e734ab3dabfb68351ad2c0618888635dcb78ca38c9eb7fb7dc30efe5c"},"schema_version":"1.0","source":{"id":"1407.6276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6276","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6276v1","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6276","created_at":"2026-05-18T01:19:00Z"},{"alias_kind":"pith_short_12","alias_value":"2KTPISX6ZDLR","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KTPISX6ZDLRFEWO","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KTPISX6","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:e47210041409f6a1178bb882b3c006c6e21c8d44f08a372807347b034e0f6559","target":"graph","created_at":"2026-05-18T01:19:00Z","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":"In his 2007 monograph, D. Christodoulou proved a remarkable result giving a detailed description of shock formation, for small $H^s$-initial conditions ($s$ sufficiently large), in solutions to the relativistic Euler equations in three space dimensions. His work provided a significant advancement over a large body of prior work concerning the long-time behavior of solutions to higher-dimensional quasilinear wave equations, initiated by F. John in the mid 1970's and continued by S. Klainerman, T. Sideris, L. H\\\"ormander, H. Lindblad, S. Alinhac, and others. Our goal in this paper is to give an ","authors_text":"Gustav Holzegel, Jared Speck, Sergiu Klainerman, Willie Wong","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T15:52:28Z","title":"Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6276","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:dcb93651ccfb914ee45bcaddb76a7ae8d472d2fbcae1583bee60eeebd4cb9d73","target":"record","created_at":"2026-05-18T01:19:00Z","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":"673ee461abec12cf699fbb0e6e3adf027c93954902dc91f8d83de049a484a904","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T15:52:28Z","title_canon_sha256":"9ed5242e734ab3dabfb68351ad2c0618888635dcb78ca38c9eb7fb7dc30efe5c"},"schema_version":"1.0","source":{"id":"1407.6276","kind":"arxiv","version":1}},"canonical_sha256":"d2a6f44afec8d71292ce813350a9782fe464445f81c443d7e34fd274f4842e7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2a6f44afec8d71292ce813350a9782fe464445f81c443d7e34fd274f4842e7d","first_computed_at":"2026-05-18T01:19:00.614962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:00.614962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYin6dHGAtR/XFFK014eofL45iEPrZfh/4Fd5QbWARX1IM9mc4fsrts68K1H8gURAzdJL0RRaqhnHp5Zpf93Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:00.615492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcb93651ccfb914ee45bcaddb76a7ae8d472d2fbcae1583bee60eeebd4cb9d73","sha256:e47210041409f6a1178bb882b3c006c6e21c8d44f08a372807347b034e0f6559"],"state_sha256":"b89f17fbc05b0fb78978b88e81ed7cf724deacdf59b9e6ae7e8f2b1582ac8a35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLmFot0A2thBjTHseXYNjl8ou6Qw+ZTA7eRQ9NjJPitLhTgTncYGfW9h2TVFeRymHKgxU+AfYj++Fc/3gl6QAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:41:37.724680Z","bundle_sha256":"64b05efd1295fdcba6f51a9c8658d6ab3b8a894f8bae75f6254e2e2c20edb6e6"}}