{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IBFPG4MWCN3KQGOETMDYHX2YLK","short_pith_number":"pith:IBFPG4MW","canonical_record":{"source":{"id":"1407.1603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T07:04:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3dc55f4a91620a35ee0d1b28dc59cc6b0358ec4cc99b78732ef5871681adcd0d","abstract_canon_sha256":"3693b883c9b73436b7317f07e2e5932ac49483f3ce7f57a2868e6a4bd1a99703"},"schema_version":"1.0"},"canonical_sha256":"404af371961376a819c49b0783df585aa359d79345567f7a8711276ee0936a03","source":{"kind":"arxiv","id":"1407.1603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1603","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1603v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1603","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"IBFPG4MWCN3K","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IBFPG4MWCN3KQGOE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IBFPG4MW","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IBFPG4MWCN3KQGOETMDYHX2YLK","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T07:04:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3dc55f4a91620a35ee0d1b28dc59cc6b0358ec4cc99b78732ef5871681adcd0d","abstract_canon_sha256":"3693b883c9b73436b7317f07e2e5932ac49483f3ce7f57a2868e6a4bd1a99703"},"schema_version":"1.0"},"canonical_sha256":"404af371961376a819c49b0783df585aa359d79345567f7a8711276ee0936a03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:10.942448Z","signature_b64":"AI3fLnkqvNBhlK6KoVVHJbJzle3jmhO5MGz1S64FIVLJ/M7c5mmOl2zxgoHjfBUWdDJ6OCyWXNAUNUnaYS0iBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"404af371961376a819c49b0783df585aa359d79345567f7a8711276ee0936a03","last_reissued_at":"2026-05-18T02:48:10.941863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:10.941863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1603","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVuwouPWdzFjva1vz8e7i9f+8tFKViUn0elq3eDIWu4eV0h4ZGyDOctpENxtTySCdLD3qqmyQViXDvM0JXCaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:39:04.960601Z"},"content_sha256":"c836bfae1325660d26c6056f5e0325f5c6c5cf823d14e4d01f902a7370a74853","schema_version":"1.0","event_id":"sha256:c836bfae1325660d26c6056f5e0325f5c6c5cf823d14e4d01f902a7370a74853"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IBFPG4MWCN3KQGOETMDYHX2YLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Sharp Sobolev--Strichartz estimate for the wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Chris Jeavons, Neal Bez","submitted_at":"2014-07-07T07:04:52Z","abstract_excerpt":"We calculate the the sharp constant and characterise the extremal initial data in $\\dot{H}^{\\frac{3}{4}}\\times\\dot{H}^{-\\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four space dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1603","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":"2026-05-18T02:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+JQtl7517Q8DFtiplhemwmUNCVzJ6Jm1prVrlVHWam3V3qGVvi2HU86nveOr/i4N9i2dludm43/33D/+0YIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:39:04.961291Z"},"content_sha256":"26ad41b8a93ecddf3dd4ad134c0a82bbd25a3db33812ed0c5f7bcf517ca3b2f0","schema_version":"1.0","event_id":"sha256:26ad41b8a93ecddf3dd4ad134c0a82bbd25a3db33812ed0c5f7bcf517ca3b2f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/bundle.json","state_url":"https://pith.science/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/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":"2026-05-26T07:39:04Z","links":{"resolver":"https://pith.science/pith/IBFPG4MWCN3KQGOETMDYHX2YLK","bundle":"https://pith.science/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/bundle.json","state":"https://pith.science/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBFPG4MWCN3KQGOETMDYHX2YLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IBFPG4MWCN3KQGOETMDYHX2YLK","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":"3693b883c9b73436b7317f07e2e5932ac49483f3ce7f57a2868e6a4bd1a99703","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T07:04:52Z","title_canon_sha256":"3dc55f4a91620a35ee0d1b28dc59cc6b0358ec4cc99b78732ef5871681adcd0d"},"schema_version":"1.0","source":{"id":"1407.1603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1603","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1603v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1603","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"IBFPG4MWCN3K","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IBFPG4MWCN3KQGOE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IBFPG4MW","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:26ad41b8a93ecddf3dd4ad134c0a82bbd25a3db33812ed0c5f7bcf517ca3b2f0","target":"graph","created_at":"2026-05-18T02:48:10Z","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 calculate the the sharp constant and characterise the extremal initial data in $\\dot{H}^{\\frac{3}{4}}\\times\\dot{H}^{-\\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four space dimensions.","authors_text":"Chris Jeavons, Neal Bez","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T07:04:52Z","title":"A Sharp Sobolev--Strichartz estimate for the wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1603","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:c836bfae1325660d26c6056f5e0325f5c6c5cf823d14e4d01f902a7370a74853","target":"record","created_at":"2026-05-18T02:48:10Z","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":"3693b883c9b73436b7317f07e2e5932ac49483f3ce7f57a2868e6a4bd1a99703","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-07T07:04:52Z","title_canon_sha256":"3dc55f4a91620a35ee0d1b28dc59cc6b0358ec4cc99b78732ef5871681adcd0d"},"schema_version":"1.0","source":{"id":"1407.1603","kind":"arxiv","version":1}},"canonical_sha256":"404af371961376a819c49b0783df585aa359d79345567f7a8711276ee0936a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"404af371961376a819c49b0783df585aa359d79345567f7a8711276ee0936a03","first_computed_at":"2026-05-18T02:48:10.941863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:10.941863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AI3fLnkqvNBhlK6KoVVHJbJzle3jmhO5MGz1S64FIVLJ/M7c5mmOl2zxgoHjfBUWdDJ6OCyWXNAUNUnaYS0iBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:10.942448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c836bfae1325660d26c6056f5e0325f5c6c5cf823d14e4d01f902a7370a74853","sha256:26ad41b8a93ecddf3dd4ad134c0a82bbd25a3db33812ed0c5f7bcf517ca3b2f0"],"state_sha256":"60f917758e636dc6dac28b4b993125611aa71f3c7efe060e9f5cbcd98186d132"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQV+R6Z5ADsiITOnkeQLVDAjI4o4yCST1crX/cNi9krKUwo9Wn0q2pHWOV1zViuhFyEaLuujTR/MNuLDi9TVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:39:04.965271Z","bundle_sha256":"3a22e210a48652aeecf5172e5d5cbe3b564072edb5692dcccf90170feb87bb24"}}