{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7RE42ALBFKJXUDYLTLXOKGYPYF","short_pith_number":"pith:7RE42ALB","canonical_record":{"source":{"id":"1109.0647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-09-03T19:40:54Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"c6db7225c0fe8dadff311e0d8d26defce4b78f1537cf9630a607abea81d55f94","abstract_canon_sha256":"50b7403deba247d054668207137ed822815d98a29dd594114daaefe6686e2648"},"schema_version":"1.0"},"canonical_sha256":"fc49cd01612a937a0f0b9aeee51b0fc141490ec6a07c3021cdb84d9d0c4a23f3","source":{"kind":"arxiv","id":"1109.0647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0647","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0647v1","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0647","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"7RE42ALBFKJX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7RE42ALBFKJXUDYL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7RE42ALB","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7RE42ALBFKJXUDYLTLXOKGYPYF","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-09-03T19:40:54Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"c6db7225c0fe8dadff311e0d8d26defce4b78f1537cf9630a607abea81d55f94","abstract_canon_sha256":"50b7403deba247d054668207137ed822815d98a29dd594114daaefe6686e2648"},"schema_version":"1.0"},"canonical_sha256":"fc49cd01612a937a0f0b9aeee51b0fc141490ec6a07c3021cdb84d9d0c4a23f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:07.151650Z","signature_b64":"B3UFSGdp7lkV4T+Als7jAT6ek9ul3j6FOjyez7FbH3T6WJdOppfFVBx/D6lVKePB+sPZrT9cIAyWquC/zqhOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc49cd01612a937a0f0b9aeee51b0fc141490ec6a07c3021cdb84d9d0c4a23f3","last_reissued_at":"2026-05-18T04:14:07.151193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:07.151193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0647","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":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AxmTt4vppy+ZDjR11fnZNS03ehwvRUECCQ6Hp/83IGh6fb42z/G/8ZYtvDYLQXM8r67ffJ+LZYV45xEwkbTADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:23:57.969978Z"},"content_sha256":"c9769da2fb930946a432bbd512cebaf8f767fdc054e839e23df571c3ba71bff8","schema_version":"1.0","event_id":"sha256:c9769da2fb930946a432bbd512cebaf8f767fdc054e839e23df571c3ba71bff8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7RE42ALBFKJXUDYLTLXOKGYPYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From nonlocal gap solitary waves to bound states in periodic media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"nlin.PS","authors_text":"Guenbo Hwang, Jianke Yang, T.R. Akylas","submitted_at":"2011-09-03T19:40:54Z","abstract_excerpt":"Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\\\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become nonlocal owing to the presence of growing tails of exponentially-small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such nonlocal solitary waves, higher-order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0647","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":"2026-05-18T04:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ip7LyZFgGkHICN1uxEeYGl01dsK1Qkh4l3tV4gSlZILrX+lS9LU8/Scjcs1c9k58b6UqUoe/Jr2fhMMhYadEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:23:57.970352Z"},"content_sha256":"be6a6df0fa5fe60d3efcb11dc4868622c80dd9f444a12e91e09569de3a0d649c","schema_version":"1.0","event_id":"sha256:be6a6df0fa5fe60d3efcb11dc4868622c80dd9f444a12e91e09569de3a0d649c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/bundle.json","state_url":"https://pith.science/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/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":"2026-05-30T07:23:57Z","links":{"resolver":"https://pith.science/pith/7RE42ALBFKJXUDYLTLXOKGYPYF","bundle":"https://pith.science/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/bundle.json","state":"https://pith.science/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RE42ALBFKJXUDYLTLXOKGYPYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7RE42ALBFKJXUDYLTLXOKGYPYF","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":"50b7403deba247d054668207137ed822815d98a29dd594114daaefe6686e2648","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-09-03T19:40:54Z","title_canon_sha256":"c6db7225c0fe8dadff311e0d8d26defce4b78f1537cf9630a607abea81d55f94"},"schema_version":"1.0","source":{"id":"1109.0647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0647","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0647v1","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0647","created_at":"2026-05-18T04:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"7RE42ALBFKJX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7RE42ALBFKJXUDYL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7RE42ALB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:be6a6df0fa5fe60d3efcb11dc4868622c80dd9f444a12e91e09569de3a0d649c","target":"graph","created_at":"2026-05-18T04:14:07Z","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":"Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\\\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become nonlocal owing to the presence of growing tails of exponentially-small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such nonlocal solitary waves, higher-order ","authors_text":"Guenbo Hwang, Jianke Yang, T.R. Akylas","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-09-03T19:40:54Z","title":"From nonlocal gap solitary waves to bound states in periodic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0647","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:c9769da2fb930946a432bbd512cebaf8f767fdc054e839e23df571c3ba71bff8","target":"record","created_at":"2026-05-18T04:14:07Z","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":"50b7403deba247d054668207137ed822815d98a29dd594114daaefe6686e2648","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2011-09-03T19:40:54Z","title_canon_sha256":"c6db7225c0fe8dadff311e0d8d26defce4b78f1537cf9630a607abea81d55f94"},"schema_version":"1.0","source":{"id":"1109.0647","kind":"arxiv","version":1}},"canonical_sha256":"fc49cd01612a937a0f0b9aeee51b0fc141490ec6a07c3021cdb84d9d0c4a23f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc49cd01612a937a0f0b9aeee51b0fc141490ec6a07c3021cdb84d9d0c4a23f3","first_computed_at":"2026-05-18T04:14:07.151193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:07.151193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3UFSGdp7lkV4T+Als7jAT6ek9ul3j6FOjyez7FbH3T6WJdOppfFVBx/D6lVKePB+sPZrT9cIAyWquC/zqhOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:07.151650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9769da2fb930946a432bbd512cebaf8f767fdc054e839e23df571c3ba71bff8","sha256:be6a6df0fa5fe60d3efcb11dc4868622c80dd9f444a12e91e09569de3a0d649c"],"state_sha256":"f312a3037059d6eaec80bf9f6440c5558a46063ca46dbd59cbb17c7d5dd4c803"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEBXwHDW55K9qnk8/wDDVnGyDcCXsf+JLINKjE+AHt+0z/nAXhTaVO57g+L7gXo3nVX2uyhilKF7EC6EeNaKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:23:57.973507Z","bundle_sha256":"7475c6786c7351331d6cf799b058d0e6e28c48cb0aaefc9a670dcb3b7f13087e"}}