{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:U42GSPY2W53VJQPSM2NCWMT42V","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":"b90bc53797a7b1f7abb6eb9fe56c7ade2cd72ec389561cc610ecf411ebaa60e3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T09:44:11Z","title_canon_sha256":"10a7c7db2f1bc173c6afb83b8ac12a1f1eb9582b6c001a312fc6543496c69642"},"schema_version":"1.0","source":{"id":"0802.2776","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2776","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2776v3","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2776","created_at":"2026-05-18T04:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"U42GSPY2W53V","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"U42GSPY2W53VJQPS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"U42GSPY2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:de372c45e5e0b58dec58c2b7024f302fc442b1cf12dca3d81f880fb45522ca59","target":"graph","created_at":"2026-05-18T04:31:20Z","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":"The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter $\\epsilon$. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic","authors_text":"Afshin Montakhab, A. Gharaati, M. Peyravi, N. Riazi","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T09:44:11Z","title":"Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2776","kind":"arxiv","version":3},"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":"sha256:2061899b21c146356a72bc3ea314b4bd6ef8b2587462f380ded9292699602607","target":"record","created_at":"2026-05-18T04:31:20Z","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":"b90bc53797a7b1f7abb6eb9fe56c7ade2cd72ec389561cc610ecf411ebaa60e3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T09:44:11Z","title_canon_sha256":"10a7c7db2f1bc173c6afb83b8ac12a1f1eb9582b6c001a312fc6543496c69642"},"schema_version":"1.0","source":{"id":"0802.2776","kind":"arxiv","version":3}},"canonical_sha256":"a734693f1ab77754c1f2669a2b327cd56188f43bf279a3668893b75b709559cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a734693f1ab77754c1f2669a2b327cd56188f43bf279a3668893b75b709559cf","first_computed_at":"2026-05-18T04:31:20.623410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:20.623410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j5RlWzmYSKnMwm3cR6f1mKpgrwiO4B4lvgeUDKBXQZhy8gE2A6m2gy/hgMem8zfv1Ai7Ja+9n2O6LohTD7zvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:20.624129Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.2776","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2061899b21c146356a72bc3ea314b4bd6ef8b2587462f380ded9292699602607","sha256:de372c45e5e0b58dec58c2b7024f302fc442b1cf12dca3d81f880fb45522ca59"],"state_sha256":"5bd74777d7e803867d1686821a8e363d2bf151c9dc3907bfd083026a628da2fc"}