{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R5U7XQS2XQDR4BBRCAY2DTYE6S","short_pith_number":"pith:R5U7XQS2","canonical_record":{"source":{"id":"1406.1527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-05T21:16:00Z","cross_cats_sorted":[],"title_canon_sha256":"d486843a8bae6fdb36990e117dfc00fec1ca9a8973fc970b85832061f4263b64","abstract_canon_sha256":"761256aa7869d9d5fb7384a79c619665e5fd7c6d06132e79a75863bcd970c30a"},"schema_version":"1.0"},"canonical_sha256":"8f69fbc25abc071e04311031a1cf04f48ea798ca21f4cdb8298f1d731e77691e","source":{"kind":"arxiv","id":"1406.1527","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1527","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1527v1","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1527","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"R5U7XQS2XQDR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5U7XQS2XQDR4BBR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5U7XQS2","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R5U7XQS2XQDR4BBRCAY2DTYE6S","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-05T21:16:00Z","cross_cats_sorted":[],"title_canon_sha256":"d486843a8bae6fdb36990e117dfc00fec1ca9a8973fc970b85832061f4263b64","abstract_canon_sha256":"761256aa7869d9d5fb7384a79c619665e5fd7c6d06132e79a75863bcd970c30a"},"schema_version":"1.0"},"canonical_sha256":"8f69fbc25abc071e04311031a1cf04f48ea798ca21f4cdb8298f1d731e77691e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:12.319921Z","signature_b64":"uu4H1TzlkiYd/nvdieYCn/R/ndGfhbYXGDYrLsNPtjCc+/IhlPd1etUjGfv+cURkAvsiAZysisOQeuxKWK+EAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f69fbc25abc071e04311031a1cf04f48ea798ca21f4cdb8298f1d731e77691e","last_reissued_at":"2026-05-18T01:20:12.319384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:12.319384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1527","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":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gIPDYFOhYgsd7gkwokZBjEWZNitFRue1z38v8tGi9HizoElrLz4aTztofs8yHrDxer3L3oZ/z5zwmIEVWC5zAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:08.079384Z"},"content_sha256":"3eeef7efd79a53eb2cface55324a60394da15480b265c0662e29817bece2eaa0","schema_version":"1.0","event_id":"sha256:3eeef7efd79a53eb2cface55324a60394da15480b265c0662e29817bece2eaa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R5U7XQS2XQDR4BBRCAY2DTYE6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonexistence of small doubly periodic solutions for dispersive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David M. Ambrose, J. Douglas Wright","submitted_at":"2014-06-05T21:16:00Z","abstract_excerpt":"We study the question of existence of time-periodic, spatially periodic solutions for dispersive evolution equations, and in particular, we introduce a framework for demonstrating the nonexistence of such solutions. We formulate the problem so that doubly periodic solutions correspond to fixed points of a certain operator. We prove that this operator is locally contracting, for almost every temporal period, if the Duhamel integral associated to the evolution exhibits a weak smoothing property. This implies the nonexistence of nontrivial, small-amplitude time-periodic solutions for almost every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1527","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":"2026-05-18T01:20:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+ODa1SMbh+obF2zr55jj8iXuD3zzv28Be+nMSPXGJY9Rcq/lk7vjfkA/HPYncKoUYd44wuaJ3gxyEz2jZ7TDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:08.079727Z"},"content_sha256":"a7f2dbba7ddceee68eba84d3c6d192896e6e60810ff0b99e49828ca67642aae5","schema_version":"1.0","event_id":"sha256:a7f2dbba7ddceee68eba84d3c6d192896e6e60810ff0b99e49828ca67642aae5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/bundle.json","state_url":"https://pith.science/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/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":"2026-06-21T02:01:08Z","links":{"resolver":"https://pith.science/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S","bundle":"https://pith.science/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/bundle.json","state":"https://pith.science/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5U7XQS2XQDR4BBRCAY2DTYE6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R5U7XQS2XQDR4BBRCAY2DTYE6S","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":"761256aa7869d9d5fb7384a79c619665e5fd7c6d06132e79a75863bcd970c30a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-05T21:16:00Z","title_canon_sha256":"d486843a8bae6fdb36990e117dfc00fec1ca9a8973fc970b85832061f4263b64"},"schema_version":"1.0","source":{"id":"1406.1527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1527","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1527v1","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1527","created_at":"2026-05-18T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"R5U7XQS2XQDR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5U7XQS2XQDR4BBR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5U7XQS2","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:a7f2dbba7ddceee68eba84d3c6d192896e6e60810ff0b99e49828ca67642aae5","target":"graph","created_at":"2026-05-18T01:20:12Z","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 study the question of existence of time-periodic, spatially periodic solutions for dispersive evolution equations, and in particular, we introduce a framework for demonstrating the nonexistence of such solutions. We formulate the problem so that doubly periodic solutions correspond to fixed points of a certain operator. We prove that this operator is locally contracting, for almost every temporal period, if the Duhamel integral associated to the evolution exhibits a weak smoothing property. This implies the nonexistence of nontrivial, small-amplitude time-periodic solutions for almost every","authors_text":"David M. Ambrose, J. Douglas Wright","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-05T21:16:00Z","title":"Nonexistence of small doubly periodic solutions for dispersive equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1527","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":"sha256:3eeef7efd79a53eb2cface55324a60394da15480b265c0662e29817bece2eaa0","target":"record","created_at":"2026-05-18T01:20:12Z","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":"761256aa7869d9d5fb7384a79c619665e5fd7c6d06132e79a75863bcd970c30a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-05T21:16:00Z","title_canon_sha256":"d486843a8bae6fdb36990e117dfc00fec1ca9a8973fc970b85832061f4263b64"},"schema_version":"1.0","source":{"id":"1406.1527","kind":"arxiv","version":1}},"canonical_sha256":"8f69fbc25abc071e04311031a1cf04f48ea798ca21f4cdb8298f1d731e77691e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f69fbc25abc071e04311031a1cf04f48ea798ca21f4cdb8298f1d731e77691e","first_computed_at":"2026-05-18T01:20:12.319384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:12.319384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uu4H1TzlkiYd/nvdieYCn/R/ndGfhbYXGDYrLsNPtjCc+/IhlPd1etUjGfv+cURkAvsiAZysisOQeuxKWK+EAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:12.319921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eeef7efd79a53eb2cface55324a60394da15480b265c0662e29817bece2eaa0","sha256:a7f2dbba7ddceee68eba84d3c6d192896e6e60810ff0b99e49828ca67642aae5"],"state_sha256":"a83b84abf492d10e13f3b1366c582960c187eaf991530e8ad663b434db03aab6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kfT86NpGl7TZ5loge0abOSKSIexd5RrQuZ8G6Ptlzl/DRcshhDUKG84cJwF9nxrl0DeP2wm8ieiexnplgI/4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:01:08.081574Z","bundle_sha256":"e163670a1c2ed48c43ad23f221199f28c2bfc92ffd774c8771e7072c1783970e"}}