{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:O6WRK2N7WJF3Q74L2WCW33WQ5E","short_pith_number":"pith:O6WRK2N7","canonical_record":{"source":{"id":"1209.3666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-17T14:31:56Z","cross_cats_sorted":[],"title_canon_sha256":"1e23f54562be905dba7ff1362e352b7ae4f521d13fbc05f69cc30583b39e53a2","abstract_canon_sha256":"a56091abc28833969435562c9a466f2c4028c56b74b6e7047b96b5f4e7fd6a8d"},"schema_version":"1.0"},"canonical_sha256":"77ad1569bfb24bb87f8bd5856deed0e92bd783f56e9d4f543f8acc9fcbe9a90a","source":{"kind":"arxiv","id":"1209.3666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3666","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3666v1","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3666","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"O6WRK2N7WJF3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O6WRK2N7WJF3Q74L","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O6WRK2N7","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:O6WRK2N7WJF3Q74L2WCW33WQ5E","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-17T14:31:56Z","cross_cats_sorted":[],"title_canon_sha256":"1e23f54562be905dba7ff1362e352b7ae4f521d13fbc05f69cc30583b39e53a2","abstract_canon_sha256":"a56091abc28833969435562c9a466f2c4028c56b74b6e7047b96b5f4e7fd6a8d"},"schema_version":"1.0"},"canonical_sha256":"77ad1569bfb24bb87f8bd5856deed0e92bd783f56e9d4f543f8acc9fcbe9a90a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.748014Z","signature_b64":"9VDzIBZ4FcrPwsGCOy6tdD+Ui36NAx3Kc/tsMxyvFdrFj9oO9U+ITGHpvMHBkvzddZp+PV9fU4VWa0FD1NLGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77ad1569bfb24bb87f8bd5856deed0e92bd783f56e9d4f543f8acc9fcbe9a90a","last_reissued_at":"2026-05-18T03:45:23.747554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.747554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3666","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":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1T4qw5Dnw88WTVj+Wav0A2/Pd7UnabhtsEi/YnvMcUHAaF9lar8ivAp8sM9+BKSsCuxw8SFXsV2PibeCWsU4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:03:55.993479Z"},"content_sha256":"bb5bd2c8ae8a48277e5ed6283b418df994f0c7dfe7d5f76742592be1e0b90233","schema_version":"1.0","event_id":"sha256:bb5bd2c8ae8a48277e5ed6283b418df994f0c7dfe7d5f76742592be1e0b90233"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:O6WRK2N7WJF3Q74L2WCW33WQ5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral stability for subsonic traveling pulses of the Boussinesq `abc' system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Atanas Stefanov, Milena Stanislavova, Sevdzhan Hakkaev","submitted_at":"2012-09-17T14:31:56Z","abstract_excerpt":"We consider the spectral stability of certain traveling wave solutions of the Boussinesq `abc' system. More precisely, we consider the explicit $sech^2(x)$ like solutions of the form\n$(\\vp(x-w t), \\psi(x- w t)=(\\vp, const. \\vp)$, exhibited by M. Chen (1998) and we provide a complete rigorous characterization of the spectral stability in all cases for which $a=c<0, b>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3666","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":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKo84wj2sGkBSLd/dlHG9TY6vHCne7lg5DLSHafbetqBQpzrI9UUjj2jucZNl42k4yWYnHpiAS6UQ90wpZp8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:03:55.993815Z"},"content_sha256":"b46c13b692ad66665d2f6794cead44e9cac250872586a6f944b63bf23e93a4a9","schema_version":"1.0","event_id":"sha256:b46c13b692ad66665d2f6794cead44e9cac250872586a6f944b63bf23e93a4a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/bundle.json","state_url":"https://pith.science/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/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":"2026-06-03T19:03:55Z","links":{"resolver":"https://pith.science/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E","bundle":"https://pith.science/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/bundle.json","state":"https://pith.science/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6WRK2N7WJF3Q74L2WCW33WQ5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O6WRK2N7WJF3Q74L2WCW33WQ5E","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":"a56091abc28833969435562c9a466f2c4028c56b74b6e7047b96b5f4e7fd6a8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-17T14:31:56Z","title_canon_sha256":"1e23f54562be905dba7ff1362e352b7ae4f521d13fbc05f69cc30583b39e53a2"},"schema_version":"1.0","source":{"id":"1209.3666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3666","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3666v1","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3666","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"O6WRK2N7WJF3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O6WRK2N7WJF3Q74L","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O6WRK2N7","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:b46c13b692ad66665d2f6794cead44e9cac250872586a6f944b63bf23e93a4a9","target":"graph","created_at":"2026-05-18T03:45:23Z","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 spectral stability of certain traveling wave solutions of the Boussinesq `abc' system. More precisely, we consider the explicit $sech^2(x)$ like solutions of the form\n$(\\vp(x-w t), \\psi(x- w t)=(\\vp, const. \\vp)$, exhibited by M. Chen (1998) and we provide a complete rigorous characterization of the spectral stability in all cases for which $a=c<0, b>0$.","authors_text":"Atanas Stefanov, Milena Stanislavova, Sevdzhan Hakkaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-17T14:31:56Z","title":"Spectral stability for subsonic traveling pulses of the Boussinesq `abc' system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3666","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:bb5bd2c8ae8a48277e5ed6283b418df994f0c7dfe7d5f76742592be1e0b90233","target":"record","created_at":"2026-05-18T03:45:23Z","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":"a56091abc28833969435562c9a466f2c4028c56b74b6e7047b96b5f4e7fd6a8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-17T14:31:56Z","title_canon_sha256":"1e23f54562be905dba7ff1362e352b7ae4f521d13fbc05f69cc30583b39e53a2"},"schema_version":"1.0","source":{"id":"1209.3666","kind":"arxiv","version":1}},"canonical_sha256":"77ad1569bfb24bb87f8bd5856deed0e92bd783f56e9d4f543f8acc9fcbe9a90a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ad1569bfb24bb87f8bd5856deed0e92bd783f56e9d4f543f8acc9fcbe9a90a","first_computed_at":"2026-05-18T03:45:23.747554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:23.747554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9VDzIBZ4FcrPwsGCOy6tdD+Ui36NAx3Kc/tsMxyvFdrFj9oO9U+ITGHpvMHBkvzddZp+PV9fU4VWa0FD1NLGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:23.748014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb5bd2c8ae8a48277e5ed6283b418df994f0c7dfe7d5f76742592be1e0b90233","sha256:b46c13b692ad66665d2f6794cead44e9cac250872586a6f944b63bf23e93a4a9"],"state_sha256":"0008a2f31d34fd12a79be0d2aab61a631afa178f4f66423f962e98e666acd2fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GNbdSXxyYs0jygrQqIPTwEjwFMdH0aHPgozqJbG4HZ5OnVRClfIqMIRaEH9G439LRm0bfnXzZJgve8hT3r1mBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:03:55.996444Z","bundle_sha256":"7815ba8310a73583b8069d3cfc8c93cd6f5e8f2ec6a112c02e897308babed136"}}