{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P3R5C2VGV5PTOH4KS2GH7KWVWA","short_pith_number":"pith:P3R5C2VG","canonical_record":{"source":{"id":"1707.01946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2017-07-06T19:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"5d56ad4ee1f092e3643fd361830bae16bf3ef84cde5d5e569959cfad208ea95d","abstract_canon_sha256":"999731107a89e81df58edfbdd6201503dd569e7766eefb39666802da2ad8322e"},"schema_version":"1.0"},"canonical_sha256":"7ee3d16aa6af5f371f8a968c7faad5b00bb7e114779e0c2bd45756dec5a2a2fb","source":{"kind":"arxiv","id":"1707.01946","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01946","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01946v2","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01946","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"P3R5C2VGV5PT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P3R5C2VGV5PTOH4K","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P3R5C2VG","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P3R5C2VGV5PTOH4KS2GH7KWVWA","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2017-07-06T19:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"5d56ad4ee1f092e3643fd361830bae16bf3ef84cde5d5e569959cfad208ea95d","abstract_canon_sha256":"999731107a89e81df58edfbdd6201503dd569e7766eefb39666802da2ad8322e"},"schema_version":"1.0"},"canonical_sha256":"7ee3d16aa6af5f371f8a968c7faad5b00bb7e114779e0c2bd45756dec5a2a2fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:54.728573Z","signature_b64":"YU1Qy3EDsRvm2TDms0uZjIUiYaSsvByWUSl3NTjL+FYIIKM1ImBd7xobnb/+czTgCnPq8ek6Qiv96uB+UTrgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ee3d16aa6af5f371f8a968c7faad5b00bb7e114779e0c2bd45756dec5a2a2fb","last_reissued_at":"2026-05-17T23:58:54.728041Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:54.728041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01946","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vVO3OykaBCId3iIYviX/zhPgjepIQ7CCYCeeV2pVur/qtrhgXqOdvGG5wHo1T2H/1Vrgago7mut/ad11JiiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:44:29.102758Z"},"content_sha256":"371a63305a2ca94ebcab6608b996b28a2eb8b4180c8683fccf82a1aebbe02387","schema_version":"1.0","event_id":"sha256:371a63305a2ca94ebcab6608b996b28a2eb8b4180c8683fccf82a1aebbe02387"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P3R5C2VGV5PTOH4KS2GH7KWVWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solitary waves in the Nonlinear Dirac Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"A. Comech, A. Saxena, J. Cuevas-Maraver, N. Boussa\\\"id, P.G. Kevrekidis, R. Lan","submitted_at":"2017-07-06T19:45:39Z","abstract_excerpt":"In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01946","kind":"arxiv","version":2},"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":"2026-05-17T23:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLltI9iXdsyPOab1NSN5TP2/I4CANgKTSdzHbYKKbHfsIPOhEPVQ5NIFS4gP2Hv9H3lcgGQl/sgeC6Y6iMsxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:44:29.103417Z"},"content_sha256":"280e21de9f3f7b99c9f29ba437f8c2d823510cddf82b9e297e978d2a11f74142","schema_version":"1.0","event_id":"sha256:280e21de9f3f7b99c9f29ba437f8c2d823510cddf82b9e297e978d2a11f74142"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/bundle.json","state_url":"https://pith.science/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/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":"2026-05-31T04:44:29Z","links":{"resolver":"https://pith.science/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA","bundle":"https://pith.science/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/bundle.json","state":"https://pith.science/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3R5C2VGV5PTOH4KS2GH7KWVWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P3R5C2VGV5PTOH4KS2GH7KWVWA","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":"999731107a89e81df58edfbdd6201503dd569e7766eefb39666802da2ad8322e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2017-07-06T19:45:39Z","title_canon_sha256":"5d56ad4ee1f092e3643fd361830bae16bf3ef84cde5d5e569959cfad208ea95d"},"schema_version":"1.0","source":{"id":"1707.01946","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01946","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01946v2","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01946","created_at":"2026-05-17T23:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"P3R5C2VGV5PT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P3R5C2VGV5PTOH4K","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P3R5C2VG","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:280e21de9f3f7b99c9f29ba437f8c2d823510cddf82b9e297e978d2a11f74142","target":"graph","created_at":"2026-05-17T23:58:54Z","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":"In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored an","authors_text":"A. Comech, A. Saxena, J. Cuevas-Maraver, N. Boussa\\\"id, P.G. Kevrekidis, R. Lan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2017-07-06T19:45:39Z","title":"Solitary waves in the Nonlinear Dirac Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01946","kind":"arxiv","version":2},"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":"sha256:371a63305a2ca94ebcab6608b996b28a2eb8b4180c8683fccf82a1aebbe02387","target":"record","created_at":"2026-05-17T23:58:54Z","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":"999731107a89e81df58edfbdd6201503dd569e7766eefb39666802da2ad8322e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2017-07-06T19:45:39Z","title_canon_sha256":"5d56ad4ee1f092e3643fd361830bae16bf3ef84cde5d5e569959cfad208ea95d"},"schema_version":"1.0","source":{"id":"1707.01946","kind":"arxiv","version":2}},"canonical_sha256":"7ee3d16aa6af5f371f8a968c7faad5b00bb7e114779e0c2bd45756dec5a2a2fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ee3d16aa6af5f371f8a968c7faad5b00bb7e114779e0c2bd45756dec5a2a2fb","first_computed_at":"2026-05-17T23:58:54.728041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:54.728041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YU1Qy3EDsRvm2TDms0uZjIUiYaSsvByWUSl3NTjL+FYIIKM1ImBd7xobnb/+czTgCnPq8ek6Qiv96uB+UTrgDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:54.728573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01946","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:371a63305a2ca94ebcab6608b996b28a2eb8b4180c8683fccf82a1aebbe02387","sha256:280e21de9f3f7b99c9f29ba437f8c2d823510cddf82b9e297e978d2a11f74142"],"state_sha256":"e206dbde016fc405e4a2c3b6977d8493128c744c9d5f9161fcb0c88d4d6d373e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nBAoPJBqzprzhXfDjLz/ysXQAmwBPd8Poh6SxIX8lHUkbz7HAMVVZ7VbpfV4yCaAfH/Bhnoq/Na2XIZFPblHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:44:29.106629Z","bundle_sha256":"7eb30023285fd244093a68c1d8952b9b191db1816c27461450622a54d13b4ac2"}}