{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4SV2XVGO4WPNRLOEDLU4FEOXAC","short_pith_number":"pith:4SV2XVGO","canonical_record":{"source":{"id":"1010.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-27T19:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"8c9278d20b4325eab4d233f187e3a37a2967e2414f386ac12b2ec6f68ad01850","abstract_canon_sha256":"0d1a4df72e3d5431dc253306d76690a48450bce9272ebf02811ea1d09575c260"},"schema_version":"1.0"},"canonical_sha256":"e4ababd4cee59ed8adc41ae9c291d700a269348318b3e168e069ff55ff95cc8c","source":{"kind":"arxiv","id":"1010.5775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5775","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5775v1","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5775","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"pith_short_12","alias_value":"4SV2XVGO4WPN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4SV2XVGO4WPNRLOE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4SV2XVGO","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4SV2XVGO4WPNRLOEDLU4FEOXAC","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-27T19:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"8c9278d20b4325eab4d233f187e3a37a2967e2414f386ac12b2ec6f68ad01850","abstract_canon_sha256":"0d1a4df72e3d5431dc253306d76690a48450bce9272ebf02811ea1d09575c260"},"schema_version":"1.0"},"canonical_sha256":"e4ababd4cee59ed8adc41ae9c291d700a269348318b3e168e069ff55ff95cc8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:15.950721Z","signature_b64":"+I2fgWWTx54zmvQeILPT+5fb7HRfuFekIC89DthMhqZZX8WwVOzUtHX1x9QQ75LmKIp2pXFCVATur5TaUsPVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4ababd4cee59ed8adc41ae9c291d700a269348318b3e168e069ff55ff95cc8c","last_reissued_at":"2026-05-18T04:38:15.950095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:15.950095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5775","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":"2026-05-18T04:38:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBtJqePWfuPNdZzP9XrWdoKN12kC+QVU1s66JxhNXkVWlU5TGVJLh+FiLKBOJtzE+VlKy+/nNBJp3eefgH6YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:53:06.312807Z"},"content_sha256":"cc8698370e823ff2d6e5d517de03e7ec588108789e5f40bb2df3aa0012f04687","schema_version":"1.0","event_id":"sha256:cc8698370e823ff2d6e5d517de03e7ec588108789e5f40bb2df3aa0012f04687"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4SV2XVGO4WPNRLOEDLU4FEOXAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of the Toda m-soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Hoffman, C.E. Wayne, G.N. Benes","submitted_at":"2010-10-27T19:44:02Z","abstract_excerpt":"We prove that multi-soliton solutions of the Toda lattice are both linearly and nonlinearly stable. Our proof uses neither the inverse spectral method nor the Lax pair of the model but instead studies the linearization of the B\\\"acklund} transformation which links the ($m-1$)-soliton solution to the $m$-soliton solution. We use this to construct a conjugation between the Toda flow linearized about an $m$-solition solution and the Toda flow linearized about the zero solution, whose stability properties can be determined by explicit calculation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5775","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":"2026-05-18T04:38:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7h4ASNoizwWlWYpWsFQwn4bZ0onXGxK/umLSfsI51RiC7s9Mev4S3zNsJQoPWu6lG8DwLYKb0Kpg94cCpqKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:53:06.313482Z"},"content_sha256":"966028dc1213077ad8f3cf9298f7f12391b0f5e67865fc7631a191267360d36d","schema_version":"1.0","event_id":"sha256:966028dc1213077ad8f3cf9298f7f12391b0f5e67865fc7631a191267360d36d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/bundle.json","state_url":"https://pith.science/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/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":"2026-05-25T08:53:06Z","links":{"resolver":"https://pith.science/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC","bundle":"https://pith.science/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/bundle.json","state":"https://pith.science/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SV2XVGO4WPNRLOEDLU4FEOXAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4SV2XVGO4WPNRLOEDLU4FEOXAC","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":"0d1a4df72e3d5431dc253306d76690a48450bce9272ebf02811ea1d09575c260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-27T19:44:02Z","title_canon_sha256":"8c9278d20b4325eab4d233f187e3a37a2967e2414f386ac12b2ec6f68ad01850"},"schema_version":"1.0","source":{"id":"1010.5775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5775","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5775v1","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5775","created_at":"2026-05-18T04:38:15Z"},{"alias_kind":"pith_short_12","alias_value":"4SV2XVGO4WPN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4SV2XVGO4WPNRLOE","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4SV2XVGO","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:966028dc1213077ad8f3cf9298f7f12391b0f5e67865fc7631a191267360d36d","target":"graph","created_at":"2026-05-18T04:38:15Z","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 prove that multi-soliton solutions of the Toda lattice are both linearly and nonlinearly stable. Our proof uses neither the inverse spectral method nor the Lax pair of the model but instead studies the linearization of the B\\\"acklund} transformation which links the ($m-1$)-soliton solution to the $m$-soliton solution. We use this to construct a conjugation between the Toda flow linearized about an $m$-solition solution and the Toda flow linearized about the zero solution, whose stability properties can be determined by explicit calculation.","authors_text":"A. Hoffman, C.E. Wayne, G.N. Benes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-27T19:44:02Z","title":"Asymptotic stability of the Toda m-soliton"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5775","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:cc8698370e823ff2d6e5d517de03e7ec588108789e5f40bb2df3aa0012f04687","target":"record","created_at":"2026-05-18T04:38:15Z","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":"0d1a4df72e3d5431dc253306d76690a48450bce9272ebf02811ea1d09575c260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-27T19:44:02Z","title_canon_sha256":"8c9278d20b4325eab4d233f187e3a37a2967e2414f386ac12b2ec6f68ad01850"},"schema_version":"1.0","source":{"id":"1010.5775","kind":"arxiv","version":1}},"canonical_sha256":"e4ababd4cee59ed8adc41ae9c291d700a269348318b3e168e069ff55ff95cc8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4ababd4cee59ed8adc41ae9c291d700a269348318b3e168e069ff55ff95cc8c","first_computed_at":"2026-05-18T04:38:15.950095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:15.950095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+I2fgWWTx54zmvQeILPT+5fb7HRfuFekIC89DthMhqZZX8WwVOzUtHX1x9QQ75LmKIp2pXFCVATur5TaUsPVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:15.950721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc8698370e823ff2d6e5d517de03e7ec588108789e5f40bb2df3aa0012f04687","sha256:966028dc1213077ad8f3cf9298f7f12391b0f5e67865fc7631a191267360d36d"],"state_sha256":"0696a660df6b3ae955eaefe5ebe54a28ae9dc077a71730fcfd69df7d6f47bf7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQ+zlcLQHWCIXiTQoeoqD1Kp3XqYcnN3p68hMT6tp7+0SNCuTdJZZU7myEoEOZmx2iyh3T7TK2VtcF1alyfmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:53:06.317236Z","bundle_sha256":"4bd43f6c0741b69d7ab53b5293abe44dfac8e46186ce5ed83e0ab9d17d0de331"}}