{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DXFEWIBUUUGF2HMJNV7S3CC25G","short_pith_number":"pith:DXFEWIBU","canonical_record":{"source":{"id":"1203.6015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-27T16:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"6f09267101cd433573a6175bfb88032e2d55be45f0ad61fdbf726a50c29b93f5","abstract_canon_sha256":"fd58ad1c8ae50b15f30c9c2f92cf7233dc93be352d5f8ab248db97bc256e306c"},"schema_version":"1.0"},"canonical_sha256":"1dca4b2034a50c5d1d896d7f2d885ae98f88ca0bd4066113f0ec4281347378c2","source":{"kind":"arxiv","id":"1203.6015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6015","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6015v1","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6015","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"DXFEWIBUUUGF","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DXFEWIBUUUGF2HMJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DXFEWIBU","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DXFEWIBUUUGF2HMJNV7S3CC25G","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-27T16:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"6f09267101cd433573a6175bfb88032e2d55be45f0ad61fdbf726a50c29b93f5","abstract_canon_sha256":"fd58ad1c8ae50b15f30c9c2f92cf7233dc93be352d5f8ab248db97bc256e306c"},"schema_version":"1.0"},"canonical_sha256":"1dca4b2034a50c5d1d896d7f2d885ae98f88ca0bd4066113f0ec4281347378c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:12.729885Z","signature_b64":"sJWhI1Vp/AGZPND6fQtgK1EuCZU3DT7BxvwzNIydiDsNxbWHjJkQSbeB15IqimyKGyej517qha8ZhfEAq/VlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dca4b2034a50c5d1d896d7f2d885ae98f88ca0bd4066113f0ec4281347378c2","last_reissued_at":"2026-05-18T03:59:12.729365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:12.729365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6015","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":"2026-05-18T03:59:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AniT0t6j+iwvGLuljJYYVR75aKBmAfhGh9x2HO10xEU8IGYhLCFEolWsqyMKo7aYHwrRUf9lDY+KVet+hLyzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:38:18.353446Z"},"content_sha256":"efa3830a5cdc34f8de5a5d7f22006390027c2bd2736a0ee20a3ac6bf7a55cdf0","schema_version":"1.0","event_id":"sha256:efa3830a5cdc34f8de5a5d7f22006390027c2bd2736a0ee20a3ac6bf7a55cdf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DXFEWIBUUUGF2HMJNV7S3CC25G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characteristic polynomials, related to the normal form of the non linear Schr\\\"{o}dinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nguyen Bich Van","submitted_at":"2012-03-27T16:32:29Z","abstract_excerpt":"We study the irreducibility of the characteristic polynomial of the energy graph of the non linear Schr\\\"{o}dinger equation (NLS). This will be useful to the verification of the second Melnikov condition for NLS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6015","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":"2026-05-18T03:59:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWOmfI2CczIppLNhksndKVbgJJpZvj00BrG1sT6U51SZ8YnSQMVK2Qmcx+Mafx2CsG4s8IwhSeiVMGpjXisuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:38:18.353792Z"},"content_sha256":"72271c6eb08e8e9be68d4c620fa2c0a10cc20f4f4dcfd430e3b24c4c0569979c","schema_version":"1.0","event_id":"sha256:72271c6eb08e8e9be68d4c620fa2c0a10cc20f4f4dcfd430e3b24c4c0569979c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/bundle.json","state_url":"https://pith.science/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/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":"2026-06-27T16:38:18Z","links":{"resolver":"https://pith.science/pith/DXFEWIBUUUGF2HMJNV7S3CC25G","bundle":"https://pith.science/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/bundle.json","state":"https://pith.science/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXFEWIBUUUGF2HMJNV7S3CC25G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DXFEWIBUUUGF2HMJNV7S3CC25G","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":"fd58ad1c8ae50b15f30c9c2f92cf7233dc93be352d5f8ab248db97bc256e306c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-27T16:32:29Z","title_canon_sha256":"6f09267101cd433573a6175bfb88032e2d55be45f0ad61fdbf726a50c29b93f5"},"schema_version":"1.0","source":{"id":"1203.6015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6015","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6015v1","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6015","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"DXFEWIBUUUGF","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DXFEWIBUUUGF2HMJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DXFEWIBU","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:72271c6eb08e8e9be68d4c620fa2c0a10cc20f4f4dcfd430e3b24c4c0569979c","target":"graph","created_at":"2026-05-18T03:59:12Z","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 irreducibility of the characteristic polynomial of the energy graph of the non linear Schr\\\"{o}dinger equation (NLS). This will be useful to the verification of the second Melnikov condition for NLS.","authors_text":"Nguyen Bich Van","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-27T16:32:29Z","title":"Characteristic polynomials, related to the normal form of the non linear Schr\\\"{o}dinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6015","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:efa3830a5cdc34f8de5a5d7f22006390027c2bd2736a0ee20a3ac6bf7a55cdf0","target":"record","created_at":"2026-05-18T03:59:12Z","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":"fd58ad1c8ae50b15f30c9c2f92cf7233dc93be352d5f8ab248db97bc256e306c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-27T16:32:29Z","title_canon_sha256":"6f09267101cd433573a6175bfb88032e2d55be45f0ad61fdbf726a50c29b93f5"},"schema_version":"1.0","source":{"id":"1203.6015","kind":"arxiv","version":1}},"canonical_sha256":"1dca4b2034a50c5d1d896d7f2d885ae98f88ca0bd4066113f0ec4281347378c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dca4b2034a50c5d1d896d7f2d885ae98f88ca0bd4066113f0ec4281347378c2","first_computed_at":"2026-05-18T03:59:12.729365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:12.729365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sJWhI1Vp/AGZPND6fQtgK1EuCZU3DT7BxvwzNIydiDsNxbWHjJkQSbeB15IqimyKGyej517qha8ZhfEAq/VlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:12.729885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efa3830a5cdc34f8de5a5d7f22006390027c2bd2736a0ee20a3ac6bf7a55cdf0","sha256:72271c6eb08e8e9be68d4c620fa2c0a10cc20f4f4dcfd430e3b24c4c0569979c"],"state_sha256":"cb30c204e8920e9a54714fcc10872c1482ff1ce1b104bcedc33cb19771480acf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61Vg8ibrRgmkkhrVqdYyKVOhJzKQRCCGkSgG1TiejbgW+kCrmx737Gek00QT8IL201UNreU15+yIskbT0LvdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:38:18.355598Z","bundle_sha256":"e38823327047f7f6620bd5e1b91f1e022f10a866e8adda68047fafbeeac7a13e"}}