{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ATUXFO3UEJI3ZGQ3E4553FGMCN","short_pith_number":"pith:ATUXFO3U","canonical_record":{"source":{"id":"1612.08703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-27T18:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"18fd82a3776771d8ff7ab2e08ff5950158b74a1c2bcf50466e5c70ae3d6b3923","abstract_canon_sha256":"9622d6b71bc8d35b10eb38e370fd425bd2ee1918f6faf9d99638d20ddf1f4840"},"schema_version":"1.0"},"canonical_sha256":"04e972bb742251bc9a1b273bdd94cc134453181010256b941233e2c54fbb0120","source":{"kind":"arxiv","id":"1612.08703","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08703","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08703v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08703","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"ATUXFO3UEJI3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATUXFO3UEJI3ZGQ3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATUXFO3U","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ATUXFO3UEJI3ZGQ3E4553FGMCN","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-27T18:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"18fd82a3776771d8ff7ab2e08ff5950158b74a1c2bcf50466e5c70ae3d6b3923","abstract_canon_sha256":"9622d6b71bc8d35b10eb38e370fd425bd2ee1918f6faf9d99638d20ddf1f4840"},"schema_version":"1.0"},"canonical_sha256":"04e972bb742251bc9a1b273bdd94cc134453181010256b941233e2c54fbb0120","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.168908Z","signature_b64":"kxYExcnB30HrUmICFTbMmG6objsvgyqKpjVY8G3PScuxEBawLqUW6VgLfvkd61P7ZwMs/CMHRI/FK645qkqaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04e972bb742251bc9a1b273bdd94cc134453181010256b941233e2c54fbb0120","last_reissued_at":"2026-05-18T00:32:14.168167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.168167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08703","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLltFptQFA9r6aGlXYzayytb9nvNsBu86KZiTy2Poufh+EEhZqByPAN/uu5jtuBvfpMQQS4ZwkeWAHO9MRuaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:35:22.889072Z"},"content_sha256":"5cae03429b37dd16d77c709d7d8876b70bae544e05df67b375658843feeef32c","schema_version":"1.0","event_id":"sha256:5cae03429b37dd16d77c709d7d8876b70bae544e05df67b375658843feeef32c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ATUXFO3UEJI3ZGQ3E4553FGMCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Maps, Continuous Approximation and Stable Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"David A. Kessler, Stanislav Burov","submitted_at":"2016-12-27T18:51:24Z","abstract_excerpt":"A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\\^o lemma, we obtain a Langevin type of equation. Specifically, we show how non-linear maps give rise to a Langevin description that involves multiplicative noise. The multiplicative nature of the noise induces an additional effective force, not present in the absence of noise. We further exploit the continuum description and provide an explicit formula for the stable distribution of the stocha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08703","kind":"arxiv","version":2},"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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIXYlrxQX/bMjLAiazMQULnplkyZ0EhkmsabxI68xRdFCc4S2mBMV2ktIfWHOz/+HB3/NdXpmhYXKnLVPs5TCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T20:35:22.889428Z"},"content_sha256":"84e3ada362f431dc56e464eebbf697ad70a678c2e3fc953d90af22620dff5bdd","schema_version":"1.0","event_id":"sha256:84e3ada362f431dc56e464eebbf697ad70a678c2e3fc953d90af22620dff5bdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/bundle.json","state_url":"https://pith.science/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/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":"2026-05-22T20:35:22Z","links":{"resolver":"https://pith.science/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN","bundle":"https://pith.science/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/bundle.json","state":"https://pith.science/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATUXFO3UEJI3ZGQ3E4553FGMCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ATUXFO3UEJI3ZGQ3E4553FGMCN","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":"9622d6b71bc8d35b10eb38e370fd425bd2ee1918f6faf9d99638d20ddf1f4840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-27T18:51:24Z","title_canon_sha256":"18fd82a3776771d8ff7ab2e08ff5950158b74a1c2bcf50466e5c70ae3d6b3923"},"schema_version":"1.0","source":{"id":"1612.08703","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08703","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08703v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08703","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"ATUXFO3UEJI3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATUXFO3UEJI3ZGQ3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATUXFO3U","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:84e3ada362f431dc56e464eebbf697ad70a678c2e3fc953d90af22620dff5bdd","target":"graph","created_at":"2026-05-18T00:32:14Z","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":"A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\\^o lemma, we obtain a Langevin type of equation. Specifically, we show how non-linear maps give rise to a Langevin description that involves multiplicative noise. The multiplicative nature of the noise induces an additional effective force, not present in the absence of noise. We further exploit the continuum description and provide an explicit formula for the stable distribution of the stocha","authors_text":"David A. Kessler, Stanislav Burov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-27T18:51:24Z","title":"Stochastic Maps, Continuous Approximation and Stable Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08703","kind":"arxiv","version":2},"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":"sha256:5cae03429b37dd16d77c709d7d8876b70bae544e05df67b375658843feeef32c","target":"record","created_at":"2026-05-18T00:32:14Z","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":"9622d6b71bc8d35b10eb38e370fd425bd2ee1918f6faf9d99638d20ddf1f4840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-12-27T18:51:24Z","title_canon_sha256":"18fd82a3776771d8ff7ab2e08ff5950158b74a1c2bcf50466e5c70ae3d6b3923"},"schema_version":"1.0","source":{"id":"1612.08703","kind":"arxiv","version":2}},"canonical_sha256":"04e972bb742251bc9a1b273bdd94cc134453181010256b941233e2c54fbb0120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04e972bb742251bc9a1b273bdd94cc134453181010256b941233e2c54fbb0120","first_computed_at":"2026-05-18T00:32:14.168167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.168167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kxYExcnB30HrUmICFTbMmG6objsvgyqKpjVY8G3PScuxEBawLqUW6VgLfvkd61P7ZwMs/CMHRI/FK645qkqaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.168908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08703","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cae03429b37dd16d77c709d7d8876b70bae544e05df67b375658843feeef32c","sha256:84e3ada362f431dc56e464eebbf697ad70a678c2e3fc953d90af22620dff5bdd"],"state_sha256":"f538332ae502e2c1b4277ba6cee22ebdb68cbbf370b53e1a4cff8556d8b32839"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBxdfvCl1ySR0JoZkCXAelP4F9+O43R/vpei2sMk56lcxlsmH+zPtogZWve0hjjKS7R6eMEovvTqQBEoTk8eDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T20:35:22.891328Z","bundle_sha256":"a698f59c2d3551ae7dd865e34e477bc5be92e326e6d15dd15176f28ba58a22c1"}}