{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:H3JUSDKY3ARN2FTK7JELBGKUP4","short_pith_number":"pith:H3JUSDKY","canonical_record":{"source":{"id":"1204.5625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-25T11:29:32Z","cross_cats_sorted":["physics.bio-ph","q-bio.PE"],"title_canon_sha256":"236e7eec1a0eacc318795e06d2df4ba38ba056cb78d95b3a11f00170d52330c8","abstract_canon_sha256":"befc81892971cf4d5c9e1271014d7a6aaada30d7973326ed1633ad3b471eef8d"},"schema_version":"1.0"},"canonical_sha256":"3ed3490d58d822dd166afa48b099547f027b83d6f8b6afc406bd308a5e4e0c6c","source":{"kind":"arxiv","id":"1204.5625","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5625","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5625v2","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5625","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"H3JUSDKY3ARN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H3JUSDKY3ARN2FTK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H3JUSDKY","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:H3JUSDKY3ARN2FTK7JELBGKUP4","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-25T11:29:32Z","cross_cats_sorted":["physics.bio-ph","q-bio.PE"],"title_canon_sha256":"236e7eec1a0eacc318795e06d2df4ba38ba056cb78d95b3a11f00170d52330c8","abstract_canon_sha256":"befc81892971cf4d5c9e1271014d7a6aaada30d7973326ed1633ad3b471eef8d"},"schema_version":"1.0"},"canonical_sha256":"3ed3490d58d822dd166afa48b099547f027b83d6f8b6afc406bd308a5e4e0c6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.219978Z","signature_b64":"iLhf6ABanLvS/zm8SmbsxZ2rTnFXngGojCho7yM16Q5BFx4jTzYmgCrfvPvUsqnnKnR15akGj76re6KDxrlfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ed3490d58d822dd166afa48b099547f027b83d6f8b6afc406bd308a5e4e0c6c","last_reissued_at":"2026-05-18T03:46:05.219347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.219347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5625","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":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lr8I52M/xDYtoaHBK4iRygJWVnXgSlSuJQYmnzw355jZ4KPtmfrVX66pxLVzbsKyzCW58LLzrNgXVeSYgZcgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:03:52.907600Z"},"content_sha256":"cda985d784f61178fe6b2fc23a76db1e17d4180ce874f04e8803c00f5f21c4e8","schema_version":"1.0","event_id":"sha256:cda985d784f61178fe6b2fc23a76db1e17d4180ce874f04e8803c00f5f21c4e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:H3JUSDKY3ARN2FTK7JELBGKUP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Demographic noise and piecewise deterministic Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","q-bio.PE"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan J. McKane, John Realpe-Gomez, Tobias Galla","submitted_at":"2012-04-25T11:29:32Z","abstract_excerpt":"We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from nonequilibrium statistical mechanics to study the influence that intrinsic noise has on the qualitative behavior of the system. We discuss the application of these concepts to the case of semiarid ecosystems. Using a system-size expansion we calculate the power spectrum of the fluctuations in the system. This predicts the existence of noise-induced oscillati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5625","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":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O0djHKV/5qCC3Kr7TugyqNSNO9iP9zxZ26T4EUfr3/JY1o+Kz+FZMXzgpC7NLS2Tp0fhlLlvsaCOBmGTwZepBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:03:52.907940Z"},"content_sha256":"cf730cc5818b78caf300dd807435e8388c35960edb1e21915b5b819d3483de3e","schema_version":"1.0","event_id":"sha256:cf730cc5818b78caf300dd807435e8388c35960edb1e21915b5b819d3483de3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/bundle.json","state_url":"https://pith.science/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/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":"2026-06-08T12:03:52Z","links":{"resolver":"https://pith.science/pith/H3JUSDKY3ARN2FTK7JELBGKUP4","bundle":"https://pith.science/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/bundle.json","state":"https://pith.science/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3JUSDKY3ARN2FTK7JELBGKUP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H3JUSDKY3ARN2FTK7JELBGKUP4","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":"befc81892971cf4d5c9e1271014d7a6aaada30d7973326ed1633ad3b471eef8d","cross_cats_sorted":["physics.bio-ph","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-25T11:29:32Z","title_canon_sha256":"236e7eec1a0eacc318795e06d2df4ba38ba056cb78d95b3a11f00170d52330c8"},"schema_version":"1.0","source":{"id":"1204.5625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5625","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5625v2","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5625","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"H3JUSDKY3ARN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H3JUSDKY3ARN2FTK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H3JUSDKY","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:cf730cc5818b78caf300dd807435e8388c35960edb1e21915b5b819d3483de3e","target":"graph","created_at":"2026-05-18T03:46:05Z","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 explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from nonequilibrium statistical mechanics to study the influence that intrinsic noise has on the qualitative behavior of the system. We discuss the application of these concepts to the case of semiarid ecosystems. Using a system-size expansion we calculate the power spectrum of the fluctuations in the system. This predicts the existence of noise-induced oscillati","authors_text":"Alan J. McKane, John Realpe-Gomez, Tobias Galla","cross_cats":["physics.bio-ph","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-25T11:29:32Z","title":"Demographic noise and piecewise deterministic Markov processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5625","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:cda985d784f61178fe6b2fc23a76db1e17d4180ce874f04e8803c00f5f21c4e8","target":"record","created_at":"2026-05-18T03:46:05Z","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":"befc81892971cf4d5c9e1271014d7a6aaada30d7973326ed1633ad3b471eef8d","cross_cats_sorted":["physics.bio-ph","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-25T11:29:32Z","title_canon_sha256":"236e7eec1a0eacc318795e06d2df4ba38ba056cb78d95b3a11f00170d52330c8"},"schema_version":"1.0","source":{"id":"1204.5625","kind":"arxiv","version":2}},"canonical_sha256":"3ed3490d58d822dd166afa48b099547f027b83d6f8b6afc406bd308a5e4e0c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ed3490d58d822dd166afa48b099547f027b83d6f8b6afc406bd308a5e4e0c6c","first_computed_at":"2026-05-18T03:46:05.219347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:05.219347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLhf6ABanLvS/zm8SmbsxZ2rTnFXngGojCho7yM16Q5BFx4jTzYmgCrfvPvUsqnnKnR15akGj76re6KDxrlfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:05.219978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cda985d784f61178fe6b2fc23a76db1e17d4180ce874f04e8803c00f5f21c4e8","sha256:cf730cc5818b78caf300dd807435e8388c35960edb1e21915b5b819d3483de3e"],"state_sha256":"fcc0b11e3573cc4252fb2c0900d8dd58a6ac8f60ee69896c7933d9257ced3f65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qnbfsmgt3NYcMbhxZdGdS58l/qAww7d200pcjLHarb5iVMywyRBYxVHAchCcfD+0XPwJ7u7PTLp5dNwCkpgoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:03:52.909844Z","bundle_sha256":"af0352aacf9d09d27032b366727302da91ba921f79621869f55ab49f94f3402d"}}