{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZTBLSGY7W2VYLZQFVBO3GVCAN4","short_pith_number":"pith:ZTBLSGY7","canonical_record":{"source":{"id":"1607.06788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-22T18:54:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"848e45aa8282ea71cf207d81e341a2e4b5477d357ed61cf47638dced00fb5b04","abstract_canon_sha256":"7164f3016473dab402f6e8761afad27097fd6fde94184495b316c2f4ceb3e361"},"schema_version":"1.0"},"canonical_sha256":"ccc2b91b1fb6ab85e605a85db354406f0db4efd54726b38bbfa8a28639b319ae","source":{"kind":"arxiv","id":"1607.06788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06788","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06788v1","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06788","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTBLSGY7W2VY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZTBLSGY7W2VYLZQF","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZTBLSGY7","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZTBLSGY7W2VYLZQFVBO3GVCAN4","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-22T18:54:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"848e45aa8282ea71cf207d81e341a2e4b5477d357ed61cf47638dced00fb5b04","abstract_canon_sha256":"7164f3016473dab402f6e8761afad27097fd6fde94184495b316c2f4ceb3e361"},"schema_version":"1.0"},"canonical_sha256":"ccc2b91b1fb6ab85e605a85db354406f0db4efd54726b38bbfa8a28639b319ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:39.094990Z","signature_b64":"q5qyjBhM8HWd4ChWc6jImJ4cr4WW2NX+9nsR3sYAV/xPzmebGSNvfmAA0gdu6q3lcFOKuVR13JyRhCFyon/+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccc2b91b1fb6ab85e605a85db354406f0db4efd54726b38bbfa8a28639b319ae","last_reissued_at":"2026-05-18T01:10:39.094499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:39.094499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06788","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":"2026-05-18T01:10:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCjgx/cAl0hZ1yCxn2Mi3+AyR/umHHIwC9slNmeKnBzls6dMU9XTPakDnPUgtfW8Vg9lkUeuIBhpkWLAgk1HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:17:38.382130Z"},"content_sha256":"3dcf16324589464461c62bae08e779261ee3698fbca3ea6a9d8fd1ab8afc1130","schema_version":"1.0","event_id":"sha256:3dcf16324589464461c62bae08e779261ee3698fbca3ea6a9d8fd1ab8afc1130"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZTBLSGY7W2VYLZQFVBO3GVCAN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boltzmannian Equilibrium in Stochastic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Charlotte Werndl, Roman Frigg","submitted_at":"2016-07-22T18:54:15Z","abstract_excerpt":"Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-varepsilon-equilibrium (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06788","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":"2026-05-18T01:10:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7/BoiMAd/4K2aCPeFNteD3l3ctfMBDmHJdvHdyeURfrYTQzw2gFzAeZEoA9Ii7pE/p2mziAaD32E5Y5N+3VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:17:38.382485Z"},"content_sha256":"7fa90d0dc30a78349372c75cc64db177a00b29f3192b5289d0d8234eec7c37c4","schema_version":"1.0","event_id":"sha256:7fa90d0dc30a78349372c75cc64db177a00b29f3192b5289d0d8234eec7c37c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/bundle.json","state_url":"https://pith.science/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/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":"2026-06-29T15:17:38Z","links":{"resolver":"https://pith.science/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4","bundle":"https://pith.science/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/bundle.json","state":"https://pith.science/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTBLSGY7W2VYLZQFVBO3GVCAN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZTBLSGY7W2VYLZQFVBO3GVCAN4","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":"7164f3016473dab402f6e8761afad27097fd6fde94184495b316c2f4ceb3e361","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-22T18:54:15Z","title_canon_sha256":"848e45aa8282ea71cf207d81e341a2e4b5477d357ed61cf47638dced00fb5b04"},"schema_version":"1.0","source":{"id":"1607.06788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06788","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06788v1","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06788","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTBLSGY7W2VY","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZTBLSGY7W2VYLZQF","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZTBLSGY7","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:7fa90d0dc30a78349372c75cc64db177a00b29f3192b5289d0d8234eec7c37c4","target":"graph","created_at":"2026-05-18T01:10:39Z","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":"Equilibrium is a central concept of statistical mechanics. In previous work we introduced the notions of a Boltzmannian alpha-epsilon-equilibrium and a Boltzmannian gamma-varepsilon-equilibrium (Werndl and Frigg 2015a, 2015b). This was done in a deterministic context. We now consider systems with a stochastic micro-dynamics and transfer these notions from the deterministic to the stochastic context. We then prove stochastic equivalents of the Dominance Theorem and the Prevalence Theorem. This establishes that also in stochastic systems equilibrium macro-regions are large in requisite sense.","authors_text":"Charlotte Werndl, Roman Frigg","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-22T18:54:15Z","title":"Boltzmannian Equilibrium in Stochastic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06788","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":"sha256:3dcf16324589464461c62bae08e779261ee3698fbca3ea6a9d8fd1ab8afc1130","target":"record","created_at":"2026-05-18T01:10:39Z","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":"7164f3016473dab402f6e8761afad27097fd6fde94184495b316c2f4ceb3e361","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-07-22T18:54:15Z","title_canon_sha256":"848e45aa8282ea71cf207d81e341a2e4b5477d357ed61cf47638dced00fb5b04"},"schema_version":"1.0","source":{"id":"1607.06788","kind":"arxiv","version":1}},"canonical_sha256":"ccc2b91b1fb6ab85e605a85db354406f0db4efd54726b38bbfa8a28639b319ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccc2b91b1fb6ab85e605a85db354406f0db4efd54726b38bbfa8a28639b319ae","first_computed_at":"2026-05-18T01:10:39.094499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:39.094499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5qyjBhM8HWd4ChWc6jImJ4cr4WW2NX+9nsR3sYAV/xPzmebGSNvfmAA0gdu6q3lcFOKuVR13JyRhCFyon/+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:39.094990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dcf16324589464461c62bae08e779261ee3698fbca3ea6a9d8fd1ab8afc1130","sha256:7fa90d0dc30a78349372c75cc64db177a00b29f3192b5289d0d8234eec7c37c4"],"state_sha256":"0d0a331ab57f3debfe7e7194d5cbc858ae67c3242eec8f20ff45bdcc38f120bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3k6lBW6vEA5JgvGd3inXkCKReLymTD+qJNQtb8mrGhIHoH890N5PZ1EPvb69zachKN8V711RYIGc3Toz3uZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:17:38.384338Z","bundle_sha256":"26ef24ea0d514083827030d5d76fb958575795bd6d0887636cb3e98300d4aa82"}}