{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LT46YW2JPCJFXCRTJ5L5PITP3N","short_pith_number":"pith:LT46YW2J","canonical_record":{"source":{"id":"0903.2703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-03-16T08:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"44505aa2228e9ae686ce435f540e27317049ca880617238fb3cc7268576f2cc0","abstract_canon_sha256":"2d031c068f241a4d5cf577dd3c0a0d8a304b98b30536df949bd344b46867b4df"},"schema_version":"1.0"},"canonical_sha256":"5cf9ec5b4978925b8a334f57d7a26fdb64ab4027dc9ccd97202d0271264c7618","source":{"kind":"arxiv","id":"0903.2703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.2703","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"0903.2703v1","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.2703","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"LT46YW2JPCJF","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LT46YW2JPCJFXCRT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LT46YW2J","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LT46YW2JPCJFXCRTJ5L5PITP3N","target":"record","payload":{"canonical_record":{"source":{"id":"0903.2703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-03-16T08:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"44505aa2228e9ae686ce435f540e27317049ca880617238fb3cc7268576f2cc0","abstract_canon_sha256":"2d031c068f241a4d5cf577dd3c0a0d8a304b98b30536df949bd344b46867b4df"},"schema_version":"1.0"},"canonical_sha256":"5cf9ec5b4978925b8a334f57d7a26fdb64ab4027dc9ccd97202d0271264c7618","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:28.094553Z","signature_b64":"z4hLRZjXVqk92Nq9Dk2sZL6QonfVPkWhwmPkO9OO/IGqsOPMG7ipFPM5kJEWsvFw/Xd93TKySalaqr6VmNuCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cf9ec5b4978925b8a334f57d7a26fdb64ab4027dc9ccd97202d0271264c7618","last_reissued_at":"2026-05-18T02:14:28.093982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:28.093982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.2703","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":"2026-05-18T02:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wwub8Z/FK3xAi8LaJYYzke54qJjUWzq/B4E4pSe40TAs/GXzo8VUIm7dcFD5GT1zNGB6veMWO9KTEi74xW51Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:21:25.544373Z"},"content_sha256":"109a29045e384fe93dc32292b98ba3585fac6e38fb986c044a9a8dbf4644ea79","schema_version":"1.0","event_id":"sha256:109a29045e384fe93dc32292b98ba3585fac6e38fb986c044a9a8dbf4644ea79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LT46YW2JPCJFXCRTJ5L5PITP3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate homotopy symmetry method and homotopy series solutions to the six-order boussinesq equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"S. Y. Lou, Xiaoyu Jiao, Yuan Gao","submitted_at":"2009-03-16T08:53:25Z","abstract_excerpt":"An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2703","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":"2026-05-18T02:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtlD/n7DMfZCXDtubHT78FrP5y6ySxqb/p3mzNLl4apDi8ZgbY8rsNJDsdZ2PkiKPQ2EIH5L9k+eQxIQv0PeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:21:25.544730Z"},"content_sha256":"eaa307f6f5735b13394dcdb1637aef8df1681f631cac54a8c2140f87d7e69ab8","schema_version":"1.0","event_id":"sha256:eaa307f6f5735b13394dcdb1637aef8df1681f631cac54a8c2140f87d7e69ab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/bundle.json","state_url":"https://pith.science/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/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":"2026-06-20T04:21:25Z","links":{"resolver":"https://pith.science/pith/LT46YW2JPCJFXCRTJ5L5PITP3N","bundle":"https://pith.science/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/bundle.json","state":"https://pith.science/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LT46YW2JPCJFXCRTJ5L5PITP3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LT46YW2JPCJFXCRTJ5L5PITP3N","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":"2d031c068f241a4d5cf577dd3c0a0d8a304b98b30536df949bd344b46867b4df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-03-16T08:53:25Z","title_canon_sha256":"44505aa2228e9ae686ce435f540e27317049ca880617238fb3cc7268576f2cc0"},"schema_version":"1.0","source":{"id":"0903.2703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.2703","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"0903.2703v1","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.2703","created_at":"2026-05-18T02:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"LT46YW2JPCJF","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LT46YW2JPCJFXCRT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LT46YW2J","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:eaa307f6f5735b13394dcdb1637aef8df1681f631cac54a8c2140f87d7e69ab8","target":"graph","created_at":"2026-05-18T02:14:28Z","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":"An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method.","authors_text":"S. Y. Lou, Xiaoyu Jiao, Yuan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-03-16T08:53:25Z","title":"Approximate homotopy symmetry method and homotopy series solutions to the six-order boussinesq equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2703","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":"sha256:109a29045e384fe93dc32292b98ba3585fac6e38fb986c044a9a8dbf4644ea79","target":"record","created_at":"2026-05-18T02:14:28Z","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":"2d031c068f241a4d5cf577dd3c0a0d8a304b98b30536df949bd344b46867b4df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-03-16T08:53:25Z","title_canon_sha256":"44505aa2228e9ae686ce435f540e27317049ca880617238fb3cc7268576f2cc0"},"schema_version":"1.0","source":{"id":"0903.2703","kind":"arxiv","version":1}},"canonical_sha256":"5cf9ec5b4978925b8a334f57d7a26fdb64ab4027dc9ccd97202d0271264c7618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cf9ec5b4978925b8a334f57d7a26fdb64ab4027dc9ccd97202d0271264c7618","first_computed_at":"2026-05-18T02:14:28.093982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:28.093982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4hLRZjXVqk92Nq9Dk2sZL6QonfVPkWhwmPkO9OO/IGqsOPMG7ipFPM5kJEWsvFw/Xd93TKySalaqr6VmNuCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:28.094553Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.2703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109a29045e384fe93dc32292b98ba3585fac6e38fb986c044a9a8dbf4644ea79","sha256:eaa307f6f5735b13394dcdb1637aef8df1681f631cac54a8c2140f87d7e69ab8"],"state_sha256":"2e83e1680f5ccf1d468db1bb8c57acb19d54d752787dea3a6f6630b587f45a10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UuPHqX0UfMyYn+c321UDl1YTnGh9vxusYoDi9jpGLp1Y9fNw5Rxw/HK8r590N7IvHEBRiAhAWqeAOezLzX/iDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:21:25.546648Z","bundle_sha256":"7566afd9591f075c48fee53c7eab2d42bfe36ac75971020e63b64edab4b3dd42"}}