{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QOUPWWF6CC443LWTDHZXFEW2AJ","short_pith_number":"pith:QOUPWWF6","canonical_record":{"source":{"id":"1906.11274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-26T18:05:14Z","cross_cats_sorted":[],"title_canon_sha256":"33934dc2efc155ef42ea8f505c8febf1ca105fbeb3f9a8fc45d67f4c811aee98","abstract_canon_sha256":"53dd165a28bafe50cf661048de2ff742377a0041f7fd5c6bb02190275c0fb337"},"schema_version":"1.0"},"canonical_sha256":"83a8fb58be10b9cdaed319f37292da026f0dcad6bd4e8ea20e904e418fe842a3","source":{"kind":"arxiv","id":"1906.11274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11274","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11274v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11274","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"QOUPWWF6CC44","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QOUPWWF6CC443LWT","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QOUPWWF6","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QOUPWWF6CC443LWTDHZXFEW2AJ","target":"record","payload":{"canonical_record":{"source":{"id":"1906.11274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-26T18:05:14Z","cross_cats_sorted":[],"title_canon_sha256":"33934dc2efc155ef42ea8f505c8febf1ca105fbeb3f9a8fc45d67f4c811aee98","abstract_canon_sha256":"53dd165a28bafe50cf661048de2ff742377a0041f7fd5c6bb02190275c0fb337"},"schema_version":"1.0"},"canonical_sha256":"83a8fb58be10b9cdaed319f37292da026f0dcad6bd4e8ea20e904e418fe842a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:07.630824Z","signature_b64":"TkoHGFwgv5w0rjdrOTr8LxV9zDPdSMSo2jnbsFPH4B0Bh29+QdEAK+ietAeOkqbLsCIBYt9J3SkkyXsXsL9/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83a8fb58be10b9cdaed319f37292da026f0dcad6bd4e8ea20e904e418fe842a3","last_reissued_at":"2026-05-17T23:42:07.630270Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:07.630270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.11274","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":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJjWQS+1ABwG7S9znOwzpRfA0K5tEHhouNPr1T0Ct0pDosvf/6CO3WoEqXRmLlF9APDsRXT+i1xng9sLlugcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:19:04.647923Z"},"content_sha256":"e091f5043ee78b07275d69ca6a4c595cc86064bcb3d0534e8f0dd5076c7bef0c","schema_version":"1.0","event_id":"sha256:e091f5043ee78b07275d69ca6a4c595cc86064bcb3d0534e8f0dd5076c7bef0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QOUPWWF6CC443LWTDHZXFEW2AJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay of small odd solutions for long range Schr\\\"odinger and Hartree equations in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mar\\'ia E. Mart\\'inez","submitted_at":"2019-06-26T18:05:14Z","abstract_excerpt":"We consider the long time asymptotics of (not necessarily small) odd solutions to the nonlinear Schr\\\"odinger equation with semi-linear and nonlocal Hartree nonlinearities, in one dimension of space. We assume data in the energy space $H^1(\\mathbb{R})$ only, and we prove decay to zero in compact regions of space as time tends to infinity. We give three different results where decay holds: semilinear NLS, NLS with a suitable potential, and defocusing Hartree. The proof is based on the use of suitable virial identities, in the spirit of nonlinear Klein-Gordon models as in Kowalczyk-Martel-Mu\\~no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11274","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":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obErxPcCs0ARVkMF0p085tNvY4gN4xdgj72y5/bjsz5644H8zEZjjbBzB9iOxrmow9n2zz9FIKOXZD0oOj+9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:19:04.648578Z"},"content_sha256":"5f18e97cd5078307ac4cf5a67a5bd393db5c49d768b1350a348d4b3af6a44f37","schema_version":"1.0","event_id":"sha256:5f18e97cd5078307ac4cf5a67a5bd393db5c49d768b1350a348d4b3af6a44f37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/bundle.json","state_url":"https://pith.science/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/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":"2026-05-28T00:19:04Z","links":{"resolver":"https://pith.science/pith/QOUPWWF6CC443LWTDHZXFEW2AJ","bundle":"https://pith.science/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/bundle.json","state":"https://pith.science/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOUPWWF6CC443LWTDHZXFEW2AJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QOUPWWF6CC443LWTDHZXFEW2AJ","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":"53dd165a28bafe50cf661048de2ff742377a0041f7fd5c6bb02190275c0fb337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-26T18:05:14Z","title_canon_sha256":"33934dc2efc155ef42ea8f505c8febf1ca105fbeb3f9a8fc45d67f4c811aee98"},"schema_version":"1.0","source":{"id":"1906.11274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11274","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11274v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11274","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"QOUPWWF6CC44","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QOUPWWF6CC443LWT","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QOUPWWF6","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:5f18e97cd5078307ac4cf5a67a5bd393db5c49d768b1350a348d4b3af6a44f37","target":"graph","created_at":"2026-05-17T23:42:07Z","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 the long time asymptotics of (not necessarily small) odd solutions to the nonlinear Schr\\\"odinger equation with semi-linear and nonlocal Hartree nonlinearities, in one dimension of space. We assume data in the energy space $H^1(\\mathbb{R})$ only, and we prove decay to zero in compact regions of space as time tends to infinity. We give three different results where decay holds: semilinear NLS, NLS with a suitable potential, and defocusing Hartree. The proof is based on the use of suitable virial identities, in the spirit of nonlinear Klein-Gordon models as in Kowalczyk-Martel-Mu\\~no","authors_text":"Mar\\'ia E. Mart\\'inez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-26T18:05:14Z","title":"Decay of small odd solutions for long range Schr\\\"odinger and Hartree equations in one dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11274","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:e091f5043ee78b07275d69ca6a4c595cc86064bcb3d0534e8f0dd5076c7bef0c","target":"record","created_at":"2026-05-17T23:42:07Z","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":"53dd165a28bafe50cf661048de2ff742377a0041f7fd5c6bb02190275c0fb337","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-26T18:05:14Z","title_canon_sha256":"33934dc2efc155ef42ea8f505c8febf1ca105fbeb3f9a8fc45d67f4c811aee98"},"schema_version":"1.0","source":{"id":"1906.11274","kind":"arxiv","version":1}},"canonical_sha256":"83a8fb58be10b9cdaed319f37292da026f0dcad6bd4e8ea20e904e418fe842a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83a8fb58be10b9cdaed319f37292da026f0dcad6bd4e8ea20e904e418fe842a3","first_computed_at":"2026-05-17T23:42:07.630270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:07.630270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkoHGFwgv5w0rjdrOTr8LxV9zDPdSMSo2jnbsFPH4B0Bh29+QdEAK+ietAeOkqbLsCIBYt9J3SkkyXsXsL9/BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:07.630824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e091f5043ee78b07275d69ca6a4c595cc86064bcb3d0534e8f0dd5076c7bef0c","sha256:5f18e97cd5078307ac4cf5a67a5bd393db5c49d768b1350a348d4b3af6a44f37"],"state_sha256":"535c65c2f92d196875e6262d3bd31bcec9ef373918644f7c14b3973fb1f300f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5S/Y2GrjFNCoHZu9/Qj6ezGbwKWd2Qkh8cweWBW+7A7krNDDvOr8vDDHtuW/oWnPUSr6Ck2GNxvDo27VU4iAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:19:04.651725Z","bundle_sha256":"df45590485e6d48ae2f8b8786c4fe33831efc18b8c67aa2d5da3890f8d4eba26"}}