{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:L3BN6YEH4MSOHEUAYOAC3X5SD4","short_pith_number":"pith:L3BN6YEH","canonical_record":{"source":{"id":"1604.00303","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T15:54:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"bd2ea1b830af0cee3903e8d351fa24c9e6a73c7f52cc9aa2e28316af415fce22","abstract_canon_sha256":"50fa9ae502fec37bdf92e5ca600a773a54e0b40e35c496772728e0eb666e97a8"},"schema_version":"1.0"},"canonical_sha256":"5ec2df6087e324e39280c3802ddfb21f0e915b607aeb2407d208ec0b92764674","source":{"kind":"arxiv","id":"1604.00303","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00303","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00303v3","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00303","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"L3BN6YEH4MSO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3BN6YEH4MSOHEUA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3BN6YEH","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:L3BN6YEH4MSOHEUAYOAC3X5SD4","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00303","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T15:54:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"bd2ea1b830af0cee3903e8d351fa24c9e6a73c7f52cc9aa2e28316af415fce22","abstract_canon_sha256":"50fa9ae502fec37bdf92e5ca600a773a54e0b40e35c496772728e0eb666e97a8"},"schema_version":"1.0"},"canonical_sha256":"5ec2df6087e324e39280c3802ddfb21f0e915b607aeb2407d208ec0b92764674","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:13.050951Z","signature_b64":"WDqkmF3yYlEP22t6Ql6kHHrMjFBQcb+NYiqzPHFInKexnu9ge90A6hq90X/eRQZnutg37miJA//eP5/N6H6bBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ec2df6087e324e39280c3802ddfb21f0e915b607aeb2407d208ec0b92764674","last_reissued_at":"2026-05-18T00:57:13.050511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:13.050511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00303","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVrEYd5xuxbbp+BFXnjJq2Ze4omBdnvGa0N5hS88dKEAxAkbATyRkRDB0Chumi1mMycYHtW3wFVxx6TJTG6+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:51:35.213792Z"},"content_sha256":"8951b0a82fa8d7806fa96a4f9cc9608baa8146804973024fca192f3e67dd25b1","schema_version":"1.0","event_id":"sha256:8951b0a82fa8d7806fa96a4f9cc9608baa8146804973024fca192f3e67dd25b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:L3BN6YEH4MSOHEUAYOAC3X5SD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mode stability of self-similar wave maps in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Irfan Glogi\\'c, Ovidiu Costin, Roland Donninger","submitted_at":"2016-04-01T15:54:35Z","abstract_excerpt":"We consider co-rotational wave maps from Minkowski space in $d+1$ dimensions to the $d$-sphere. Recently, Bizo\\'n and Biernat found explicit self-similar solutions for each dimension $d\\geq 4$. We give a rigorous proof for the mode stability of these self-similar wave maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00303","kind":"arxiv","version":3},"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":"2026-05-18T00:57:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yN0fLYmzMKxhCNw+gQa3Pj+5WpjIb5qFOB48dWJU+HY4LhWieKhevXFJltbQ12D9GOnPiq+pJfQLn3QQDE2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:51:35.214166Z"},"content_sha256":"5eb4d2995fdb7486603e23819a8d9ad419dc240da4dbf947b5367ad36099ca61","schema_version":"1.0","event_id":"sha256:5eb4d2995fdb7486603e23819a8d9ad419dc240da4dbf947b5367ad36099ca61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/bundle.json","state_url":"https://pith.science/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/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":"2026-05-24T04:51:35Z","links":{"resolver":"https://pith.science/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4","bundle":"https://pith.science/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/bundle.json","state":"https://pith.science/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3BN6YEH4MSOHEUAYOAC3X5SD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L3BN6YEH4MSOHEUAYOAC3X5SD4","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":"50fa9ae502fec37bdf92e5ca600a773a54e0b40e35c496772728e0eb666e97a8","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T15:54:35Z","title_canon_sha256":"bd2ea1b830af0cee3903e8d351fa24c9e6a73c7f52cc9aa2e28316af415fce22"},"schema_version":"1.0","source":{"id":"1604.00303","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00303","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00303v3","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00303","created_at":"2026-05-18T00:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"L3BN6YEH4MSO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L3BN6YEH4MSOHEUA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L3BN6YEH","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:5eb4d2995fdb7486603e23819a8d9ad419dc240da4dbf947b5367ad36099ca61","target":"graph","created_at":"2026-05-18T00:57:13Z","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 consider co-rotational wave maps from Minkowski space in $d+1$ dimensions to the $d$-sphere. Recently, Bizo\\'n and Biernat found explicit self-similar solutions for each dimension $d\\geq 4$. We give a rigorous proof for the mode stability of these self-similar wave maps.","authors_text":"Irfan Glogi\\'c, Ovidiu Costin, Roland Donninger","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T15:54:35Z","title":"Mode stability of self-similar wave maps in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00303","kind":"arxiv","version":3},"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":"sha256:8951b0a82fa8d7806fa96a4f9cc9608baa8146804973024fca192f3e67dd25b1","target":"record","created_at":"2026-05-18T00:57:13Z","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":"50fa9ae502fec37bdf92e5ca600a773a54e0b40e35c496772728e0eb666e97a8","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T15:54:35Z","title_canon_sha256":"bd2ea1b830af0cee3903e8d351fa24c9e6a73c7f52cc9aa2e28316af415fce22"},"schema_version":"1.0","source":{"id":"1604.00303","kind":"arxiv","version":3}},"canonical_sha256":"5ec2df6087e324e39280c3802ddfb21f0e915b607aeb2407d208ec0b92764674","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ec2df6087e324e39280c3802ddfb21f0e915b607aeb2407d208ec0b92764674","first_computed_at":"2026-05-18T00:57:13.050511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:13.050511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDqkmF3yYlEP22t6Ql6kHHrMjFBQcb+NYiqzPHFInKexnu9ge90A6hq90X/eRQZnutg37miJA//eP5/N6H6bBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:13.050951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00303","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8951b0a82fa8d7806fa96a4f9cc9608baa8146804973024fca192f3e67dd25b1","sha256:5eb4d2995fdb7486603e23819a8d9ad419dc240da4dbf947b5367ad36099ca61"],"state_sha256":"9981de3d9513f7bc7003a5f9484ca2b7067680ead0aaea817d27ca413691c7a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wo6SoTOxtm/4sCl6zAuR7mjVtyqzKQWFwr/JF2sRznBplateUsxfcN6Nhe9Yyj3NGtPStoHDoQi94XitxlI9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T04:51:35.216566Z","bundle_sha256":"111f1efee28c6f33b9d5c8bb14d5f628afc7a32329eb6fc30be3d21cfd666838"}}