{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:H733URQPC32HHFOQ3OCRKR34PG","short_pith_number":"pith:H733URQP","canonical_record":{"source":{"id":"1209.6552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-28T15:55:40Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9a6119c4751cc20625f56ee6075c04ca556cbf6ae2e3bdd92c47e67cfbdafc77","abstract_canon_sha256":"3df88a2e9d34723eaee36280406b80fbac5027ae2726fd8d8b15833ed6caa1ab"},"schema_version":"1.0"},"canonical_sha256":"3ff7ba460f16f47395d0db8515477c79a83327d9f724286e1c8718f42afc0ccd","source":{"kind":"arxiv","id":"1209.6552","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6552","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6552v3","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6552","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"H733URQPC32H","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H733URQPC32HHFOQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H733URQP","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:H733URQPC32HHFOQ3OCRKR34PG","target":"record","payload":{"canonical_record":{"source":{"id":"1209.6552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-28T15:55:40Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"9a6119c4751cc20625f56ee6075c04ca556cbf6ae2e3bdd92c47e67cfbdafc77","abstract_canon_sha256":"3df88a2e9d34723eaee36280406b80fbac5027ae2726fd8d8b15833ed6caa1ab"},"schema_version":"1.0"},"canonical_sha256":"3ff7ba460f16f47395d0db8515477c79a83327d9f724286e1c8718f42afc0ccd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:28.915012Z","signature_b64":"GPdl4JSObnObkNHylEhlDrOSIH6SEazfD8RBSVRdQR82g534l9AesCMFVg0yeoK07+jwvYBwR+zdrujuQuMCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ff7ba460f16f47395d0db8515477c79a83327d9f724286e1c8718f42afc0ccd","last_reissued_at":"2026-05-18T03:41:28.914412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:28.914412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.6552","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8j9LMD/le7beWanxBFOhoTaIxtfSBHs+Kk+SRUGmlGKUOP9XF+/OUAHcz8V7dFRpGRmv0Sv2OXVXe+R/1yGSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:44:46.094740Z"},"content_sha256":"a337ba926fb2de7cd4840b6c935b20664278b25c897ca527bc3b0ff7d1bac05b","schema_version":"1.0","event_id":"sha256:a337ba926fb2de7cd4840b6c935b20664278b25c897ca527bc3b0ff7d1bac05b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:H733URQPC32HHFOQ3OCRKR34PG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete conditions of Lyapunov stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Eugene Polulyakh, Igor Vlasenko, Vladimir Sharko","submitted_at":"2012-09-28T15:55:40Z","abstract_excerpt":"We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right part of the differential equation instead of conditions on a Lyapunov function along trajectories of the equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6552","kind":"arxiv","version":3},"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":"2026-05-18T03:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpTVbOkfXTFhAvArlEf+jOPdJg5/ETXZUzP8/aOVT9jLL9wiU9onbuiX4JowOeDCqgUHp7vv4F/wvYIQ9GkmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:44:46.095086Z"},"content_sha256":"669e0ec17c6cd704db8b661ef06e4425eb508187ef0dd3887ba0e0058177dc85","schema_version":"1.0","event_id":"sha256:669e0ec17c6cd704db8b661ef06e4425eb508187ef0dd3887ba0e0058177dc85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H733URQPC32HHFOQ3OCRKR34PG/bundle.json","state_url":"https://pith.science/pith/H733URQPC32HHFOQ3OCRKR34PG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H733URQPC32HHFOQ3OCRKR34PG/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":"2026-06-26T08:44:46Z","links":{"resolver":"https://pith.science/pith/H733URQPC32HHFOQ3OCRKR34PG","bundle":"https://pith.science/pith/H733URQPC32HHFOQ3OCRKR34PG/bundle.json","state":"https://pith.science/pith/H733URQPC32HHFOQ3OCRKR34PG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H733URQPC32HHFOQ3OCRKR34PG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H733URQPC32HHFOQ3OCRKR34PG","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":"3df88a2e9d34723eaee36280406b80fbac5027ae2726fd8d8b15833ed6caa1ab","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-28T15:55:40Z","title_canon_sha256":"9a6119c4751cc20625f56ee6075c04ca556cbf6ae2e3bdd92c47e67cfbdafc77"},"schema_version":"1.0","source":{"id":"1209.6552","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6552","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6552v3","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6552","created_at":"2026-05-18T03:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"H733URQPC32H","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H733URQPC32HHFOQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H733URQP","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:669e0ec17c6cd704db8b661ef06e4425eb508187ef0dd3887ba0e0058177dc85","target":"graph","created_at":"2026-05-18T03:41:28Z","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":"We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right part of the differential equation instead of conditions on a Lyapunov function along trajectories of the equation.","authors_text":"Eugene Polulyakh, Igor Vlasenko, Vladimir Sharko","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-28T15:55:40Z","title":"Discrete conditions of Lyapunov stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6552","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:a337ba926fb2de7cd4840b6c935b20664278b25c897ca527bc3b0ff7d1bac05b","target":"record","created_at":"2026-05-18T03:41:28Z","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":"3df88a2e9d34723eaee36280406b80fbac5027ae2726fd8d8b15833ed6caa1ab","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-28T15:55:40Z","title_canon_sha256":"9a6119c4751cc20625f56ee6075c04ca556cbf6ae2e3bdd92c47e67cfbdafc77"},"schema_version":"1.0","source":{"id":"1209.6552","kind":"arxiv","version":3}},"canonical_sha256":"3ff7ba460f16f47395d0db8515477c79a83327d9f724286e1c8718f42afc0ccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ff7ba460f16f47395d0db8515477c79a83327d9f724286e1c8718f42afc0ccd","first_computed_at":"2026-05-18T03:41:28.914412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:28.914412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GPdl4JSObnObkNHylEhlDrOSIH6SEazfD8RBSVRdQR82g534l9AesCMFVg0yeoK07+jwvYBwR+zdrujuQuMCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:28.915012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6552","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a337ba926fb2de7cd4840b6c935b20664278b25c897ca527bc3b0ff7d1bac05b","sha256:669e0ec17c6cd704db8b661ef06e4425eb508187ef0dd3887ba0e0058177dc85"],"state_sha256":"82ccf288ea7d54950a1817e3bd539b75be6dac3537c525581b2d743a957d5df5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AORCBHzPn+yOp72hxAJcKt5Ql+kW0/pcCIdWd7in2VhDZWD220aQoHASmjeX/Z2ji+te7KKcLNz3Btmt31abCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:44:46.097177Z","bundle_sha256":"9dc880114c9e5786551c05ea2941f892db57742374e9344ee89744e8d7407176"}}