{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CF5OD7ECDJDJLB3YN4J6S2UXAX","short_pith_number":"pith:CF5OD7EC","canonical_record":{"source":{"id":"1606.02137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-07T13:45:03Z","cross_cats_sorted":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"title_canon_sha256":"451cd0ffef019ec0d9dc9722b33ff7f5d715b37c303e55e2d85f526b48d4e0fe","abstract_canon_sha256":"4fa8c21e5d90346093c24e3a49015b8884ef5e406646a907696a257aa8beb1b1"},"schema_version":"1.0"},"canonical_sha256":"117ae1fc821a469587786f13e96a9705dfb55e0bc604758803785ab77417fd7c","source":{"kind":"arxiv","id":"1606.02137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02137","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02137v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02137","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"CF5OD7ECDJDJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CF5OD7ECDJDJLB3Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CF5OD7EC","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CF5OD7ECDJDJLB3YN4J6S2UXAX","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-07T13:45:03Z","cross_cats_sorted":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"title_canon_sha256":"451cd0ffef019ec0d9dc9722b33ff7f5d715b37c303e55e2d85f526b48d4e0fe","abstract_canon_sha256":"4fa8c21e5d90346093c24e3a49015b8884ef5e406646a907696a257aa8beb1b1"},"schema_version":"1.0"},"canonical_sha256":"117ae1fc821a469587786f13e96a9705dfb55e0bc604758803785ab77417fd7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:24.362481Z","signature_b64":"qXfRVVTmGUu7FA8GrggOWapgmV0WlbFoz+iXSIao5AQfDAVQujfsyUXgHkEFZLzbG4DikltS7BApzr3S47AFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"117ae1fc821a469587786f13e96a9705dfb55e0bc604758803785ab77417fd7c","last_reissued_at":"2026-05-18T00:04:24.361817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:24.361817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02137","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":"2026-05-18T00:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1l6nOhfabZcsR2ToN3qFhrv7+uhdMoEPVuADOYzTmWZu8ChW5SHH4RvgbNzoo50F7FnfOmV5w3r/gpG+RvJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:55:19.118213Z"},"content_sha256":"40fd7437bb42985f0278b6721941e54f184188feac07f8b0180fb43d9ae48c1a","schema_version":"1.0","event_id":"sha256:40fd7437bb42985f0278b6721941e54f184188feac07f8b0180fb43d9ae48c1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CF5OD7ECDJDJLB3YN4J6S2UXAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A functional calculus for the magnetization dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Julien Tranchida, Pascal Thibaudeau, Stam Nicolis","submitted_at":"2016-06-07T13:45:03Z","abstract_excerpt":"A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master equation for the stochastic magnetization dynamics, that is applied to both, Markovian and non-Markovian dynamics. The formalism is applied for studying different kinds of interactions, that are of practical relevance and hierarchies of evolution equations for the moments of the distribution of the magnetization are obtained. In each case, assumptions are spel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02137","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":"2026-05-18T00:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5RMPEQmnRuWrFAmsIzQk1jigg4v0h0ms5GufElbEt3zaR969h5Z4Q3w8d058gshOK8WOJyNq7yhodFkOtQLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:55:19.118590Z"},"content_sha256":"deb4acd518f64a768b0cd820e14925b6166c58e691ed59baa9b3d610f6ca8041","schema_version":"1.0","event_id":"sha256:deb4acd518f64a768b0cd820e14925b6166c58e691ed59baa9b3d610f6ca8041"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/bundle.json","state_url":"https://pith.science/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/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":"2026-06-25T23:55:19Z","links":{"resolver":"https://pith.science/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX","bundle":"https://pith.science/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/bundle.json","state":"https://pith.science/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CF5OD7ECDJDJLB3YN4J6S2UXAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CF5OD7ECDJDJLB3YN4J6S2UXAX","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":"4fa8c21e5d90346093c24e3a49015b8884ef5e406646a907696a257aa8beb1b1","cross_cats_sorted":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-07T13:45:03Z","title_canon_sha256":"451cd0ffef019ec0d9dc9722b33ff7f5d715b37c303e55e2d85f526b48d4e0fe"},"schema_version":"1.0","source":{"id":"1606.02137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02137","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02137v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02137","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"CF5OD7ECDJDJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CF5OD7ECDJDJLB3Y","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CF5OD7EC","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:deb4acd518f64a768b0cd820e14925b6166c58e691ed59baa9b3d610f6ca8041","target":"graph","created_at":"2026-05-18T00:04:24Z","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 functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master equation for the stochastic magnetization dynamics, that is applied to both, Markovian and non-Markovian dynamics. The formalism is applied for studying different kinds of interactions, that are of practical relevance and hierarchies of evolution equations for the moments of the distribution of the magnetization are obtained. In each case, assumptions are spel","authors_text":"Julien Tranchida, Pascal Thibaudeau, Stam Nicolis","cross_cats":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-07T13:45:03Z","title":"A functional calculus for the magnetization dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02137","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":"sha256:40fd7437bb42985f0278b6721941e54f184188feac07f8b0180fb43d9ae48c1a","target":"record","created_at":"2026-05-18T00:04:24Z","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":"4fa8c21e5d90346093c24e3a49015b8884ef5e406646a907696a257aa8beb1b1","cross_cats_sorted":["cond-mat.mtrl-sci","hep-lat","nlin.CD","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-07T13:45:03Z","title_canon_sha256":"451cd0ffef019ec0d9dc9722b33ff7f5d715b37c303e55e2d85f526b48d4e0fe"},"schema_version":"1.0","source":{"id":"1606.02137","kind":"arxiv","version":1}},"canonical_sha256":"117ae1fc821a469587786f13e96a9705dfb55e0bc604758803785ab77417fd7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"117ae1fc821a469587786f13e96a9705dfb55e0bc604758803785ab77417fd7c","first_computed_at":"2026-05-18T00:04:24.361817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.361817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qXfRVVTmGUu7FA8GrggOWapgmV0WlbFoz+iXSIao5AQfDAVQujfsyUXgHkEFZLzbG4DikltS7BApzr3S47AFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.362481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40fd7437bb42985f0278b6721941e54f184188feac07f8b0180fb43d9ae48c1a","sha256:deb4acd518f64a768b0cd820e14925b6166c58e691ed59baa9b3d610f6ca8041"],"state_sha256":"059d8b0c0c7d83997478e23d038e13068bfbd78787cd582616bb112ee4b42827"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbuB6wRgk43rzikkSVcTXrrfSQmNoigsQlWKw9Cdh0GKgaws+kMeICYp4UcaQWieeYFTe7Hol/4weVguRRZIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:55:19.120594Z","bundle_sha256":"a6b0736f94b7ba19ce8493dedc16a87ee6705a7591bdc143b61d05db2c7e0f6b"}}