{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Y6MBMMKPNIAZ5GBFVI27HXZSBM","short_pith_number":"pith:Y6MBMMKP","canonical_record":{"source":{"id":"1509.05737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-18T18:19:49Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"title_canon_sha256":"de5cb53b033dc79a0be36ee4d68bff0af2f781facc3575ebb3b0165622f9b84d","abstract_canon_sha256":"8b701a255378c17f7b1d1532e1b29cfdcd236decf8209bae60ab96e3673fbc08"},"schema_version":"1.0"},"canonical_sha256":"c79816314f6a019e9825aa35f3df320b3b30b381c5b85728c77ba6007447cd90","source":{"kind":"arxiv","id":"1509.05737","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05737","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05737v3","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05737","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y6MBMMKPNIAZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6MBMMKPNIAZ5GBF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6MBMMKP","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Y6MBMMKPNIAZ5GBFVI27HXZSBM","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-18T18:19:49Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"title_canon_sha256":"de5cb53b033dc79a0be36ee4d68bff0af2f781facc3575ebb3b0165622f9b84d","abstract_canon_sha256":"8b701a255378c17f7b1d1532e1b29cfdcd236decf8209bae60ab96e3673fbc08"},"schema_version":"1.0"},"canonical_sha256":"c79816314f6a019e9825aa35f3df320b3b30b381c5b85728c77ba6007447cd90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:25.269814Z","signature_b64":"5z59D+PcDE89TJ+nreLquHHcTZA76QkbwdL7Y8MIscT5xgiT/kuWrXkHt6FEb45Jl4snqA+fNBdHtpiwZBmqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c79816314f6a019e9825aa35f3df320b3b30b381c5b85728c77ba6007447cd90","last_reissued_at":"2026-05-18T01:11:25.269185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:25.269185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05737","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":"2026-05-18T01:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bDtACZeOE/YlXAjXsqGO+Uz3eIlpGIJomNs7Oug3oHTXdxPObe59+sW+InKpdZ4MJqAdwhF5HknCsJnR6ElUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:43:33.323070Z"},"content_sha256":"981231d2e2d28a28883000c80f827c32c5ec9c70cd5fcee9cfa6c686679e3285","schema_version":"1.0","event_id":"sha256:981231d2e2d28a28883000c80f827c32c5ec9c70cd5fcee9cfa6c686679e3285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Y6MBMMKPNIAZ5GBFVI27HXZSBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Analogue of the May-Wigner Instability Transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"primary_cat":"cond-mat.dis-nn","authors_text":"Boris A. Khoruzhenko, Yan V. Fyodorov","submitted_at":"2015-09-18T18:19:49Z","abstract_excerpt":"We study a system of $N\\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate $\\mu$. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically non-trivial regime characterised by an exponential number of equilibria, the vast majority of which are expected to be u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05737","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":"2026-05-18T01:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"usz8Ljy49bctUO7dICjNybGJcoVFhEQcTw2Zrkr6MXejXR5VRxr1tBdgxDNQ9GJq0otn+Giiqr7eqJLZfIE+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:43:33.323659Z"},"content_sha256":"88f11e7548db8d020407731da0d5ddebf2adc0222cd09daf237cc87fe22660e5","schema_version":"1.0","event_id":"sha256:88f11e7548db8d020407731da0d5ddebf2adc0222cd09daf237cc87fe22660e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/bundle.json","state_url":"https://pith.science/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/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":"2026-06-01T01:43:33Z","links":{"resolver":"https://pith.science/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM","bundle":"https://pith.science/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/bundle.json","state":"https://pith.science/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y6MBMMKPNIAZ5GBFVI27HXZSBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Y6MBMMKPNIAZ5GBFVI27HXZSBM","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":"8b701a255378c17f7b1d1532e1b29cfdcd236decf8209bae60ab96e3673fbc08","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-18T18:19:49Z","title_canon_sha256":"de5cb53b033dc79a0be36ee4d68bff0af2f781facc3575ebb3b0165622f9b84d"},"schema_version":"1.0","source":{"id":"1509.05737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05737","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05737v3","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05737","created_at":"2026-05-18T01:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y6MBMMKPNIAZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y6MBMMKPNIAZ5GBF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y6MBMMKP","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:88f11e7548db8d020407731da0d5ddebf2adc0222cd09daf237cc87fe22660e5","target":"graph","created_at":"2026-05-18T01:11:25Z","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 study a system of $N\\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate $\\mu$. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically non-trivial regime characterised by an exponential number of equilibria, the vast majority of which are expected to be u","authors_text":"Boris A. Khoruzhenko, Yan V. Fyodorov","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-18T18:19:49Z","title":"Nonlinear Analogue of the May-Wigner Instability Transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05737","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":"sha256:981231d2e2d28a28883000c80f827c32c5ec9c70cd5fcee9cfa6c686679e3285","target":"record","created_at":"2026-05-18T01:11:25Z","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":"8b701a255378c17f7b1d1532e1b29cfdcd236decf8209bae60ab96e3673fbc08","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.AO","physics.bio-ph","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-18T18:19:49Z","title_canon_sha256":"de5cb53b033dc79a0be36ee4d68bff0af2f781facc3575ebb3b0165622f9b84d"},"schema_version":"1.0","source":{"id":"1509.05737","kind":"arxiv","version":3}},"canonical_sha256":"c79816314f6a019e9825aa35f3df320b3b30b381c5b85728c77ba6007447cd90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c79816314f6a019e9825aa35f3df320b3b30b381c5b85728c77ba6007447cd90","first_computed_at":"2026-05-18T01:11:25.269185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:25.269185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5z59D+PcDE89TJ+nreLquHHcTZA76QkbwdL7Y8MIscT5xgiT/kuWrXkHt6FEb45Jl4snqA+fNBdHtpiwZBmqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:25.269814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:981231d2e2d28a28883000c80f827c32c5ec9c70cd5fcee9cfa6c686679e3285","sha256:88f11e7548db8d020407731da0d5ddebf2adc0222cd09daf237cc87fe22660e5"],"state_sha256":"dd269f9985ac7ddc25b4875c57c252f933acc293cec9f2cb9d6cbe38b474e16c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQLm3hTE4yCCmBnft+7c79jRMDUNO0+NoBdvHezZeFhPAf4PbMGOOSGOTGQTtVqWqlgeEdgG0Qav8Avkxk5bBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:43:33.327711Z","bundle_sha256":"7e5c0a6defa12f936fc724875b3f1f33ee823c4fa0b7c3cb3d4d841b53f864c4"}}