{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CUTUFTJSIEELJ4JN3C4F67FA5M","short_pith_number":"pith:CUTUFTJS","canonical_record":{"source":{"id":"1010.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-11T17:13:45Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"fb257253800454835a391fa6fb1a5c6c556b53dbc6560538abde461630e79450","abstract_canon_sha256":"a51450112a1b2dc337ea30350ff2d1b82b497756f582e5e5dc773c2eba433721"},"schema_version":"1.0"},"canonical_sha256":"152742cd324108b4f12dd8b85f7ca0eb2b3cecf2e9d36278bae7d05e53cea76b","source":{"kind":"arxiv","id":"1010.2162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2162","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2162v1","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2162","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"CUTUFTJSIEEL","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CUTUFTJSIEELJ4JN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CUTUFTJS","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CUTUFTJSIEELJ4JN3C4F67FA5M","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-11T17:13:45Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"fb257253800454835a391fa6fb1a5c6c556b53dbc6560538abde461630e79450","abstract_canon_sha256":"a51450112a1b2dc337ea30350ff2d1b82b497756f582e5e5dc773c2eba433721"},"schema_version":"1.0"},"canonical_sha256":"152742cd324108b4f12dd8b85f7ca0eb2b3cecf2e9d36278bae7d05e53cea76b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:11.684263Z","signature_b64":"zkj28Ytl0fGynhQMiFKlqywC1V+VvAhuWzsMlAJ0A7+cJdF83rpyzSzeFithbq1H3G0bO8IUaQ/N1zMJapu+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"152742cd324108b4f12dd8b85f7ca0eb2b3cecf2e9d36278bae7d05e53cea76b","last_reissued_at":"2026-05-18T03:01:11.683747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:11.683747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2162","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":"2026-05-18T03:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzHoSDTSL50s+hSMozYCmI6QTgeu9Ozq8/Wbf5GsiLCgKFjq6ocmyj18tjosg0WrtfGTw/X6nVgNiKgeejM8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:59:15.328979Z"},"content_sha256":"4af27a9bc90fe6262cba42f38bb9dbbcbfdde0cbf9db2487102516717eae1716","schema_version":"1.0","event_id":"sha256:4af27a9bc90fe6262cba42f38bb9dbbcbfdde0cbf9db2487102516717eae1716"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CUTUFTJSIEELJ4JN3C4F67FA5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Induced topological pressure for countable state Markov shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Johannes Jaerisch, Marc Kesseb\\\"ohmer, Sanaz Lamei","submitted_at":"2010-10-11T17:13:45Z","abstract_excerpt":"We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to important thermodynamical quantities, which are usually given only implicitly by certain identities involving the classically defined pressure. In this context we generalise Savchenko's definition of entropy for special flows to a corresponding notion of topological pressure and show that this new notion coincides with the induced pressure for a large class of H\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2162","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":"2026-05-18T03:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+UhYmlnD/FDuuN6wWbzNsXdXNJCjUNP9cJb/1AaWPd5RVD3zgJ30XbM/U75VSQHeYhJfGGsLarESRjWRUgGxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:59:15.329347Z"},"content_sha256":"cf76e54ffe6acc729ee8631e1e0100d7619d9072e433195e686b7d402a0026e3","schema_version":"1.0","event_id":"sha256:cf76e54ffe6acc729ee8631e1e0100d7619d9072e433195e686b7d402a0026e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/bundle.json","state_url":"https://pith.science/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/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":"2026-06-23T07:59:15Z","links":{"resolver":"https://pith.science/pith/CUTUFTJSIEELJ4JN3C4F67FA5M","bundle":"https://pith.science/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/bundle.json","state":"https://pith.science/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUTUFTJSIEELJ4JN3C4F67FA5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CUTUFTJSIEELJ4JN3C4F67FA5M","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":"a51450112a1b2dc337ea30350ff2d1b82b497756f582e5e5dc773c2eba433721","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-11T17:13:45Z","title_canon_sha256":"fb257253800454835a391fa6fb1a5c6c556b53dbc6560538abde461630e79450"},"schema_version":"1.0","source":{"id":"1010.2162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2162","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2162v1","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2162","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"CUTUFTJSIEEL","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CUTUFTJSIEELJ4JN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CUTUFTJS","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:cf76e54ffe6acc729ee8631e1e0100d7619d9072e433195e686b7d402a0026e3","target":"graph","created_at":"2026-05-18T03:01:11Z","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 introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to important thermodynamical quantities, which are usually given only implicitly by certain identities involving the classically defined pressure. In this context we generalise Savchenko's definition of entropy for special flows to a corresponding notion of topological pressure and show that this new notion coincides with the induced pressure for a large class of H\\","authors_text":"Johannes Jaerisch, Marc Kesseb\\\"ohmer, Sanaz Lamei","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-11T17:13:45Z","title":"Induced topological pressure for countable state Markov shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2162","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":"sha256:4af27a9bc90fe6262cba42f38bb9dbbcbfdde0cbf9db2487102516717eae1716","target":"record","created_at":"2026-05-18T03:01:11Z","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":"a51450112a1b2dc337ea30350ff2d1b82b497756f582e5e5dc773c2eba433721","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-11T17:13:45Z","title_canon_sha256":"fb257253800454835a391fa6fb1a5c6c556b53dbc6560538abde461630e79450"},"schema_version":"1.0","source":{"id":"1010.2162","kind":"arxiv","version":1}},"canonical_sha256":"152742cd324108b4f12dd8b85f7ca0eb2b3cecf2e9d36278bae7d05e53cea76b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"152742cd324108b4f12dd8b85f7ca0eb2b3cecf2e9d36278bae7d05e53cea76b","first_computed_at":"2026-05-18T03:01:11.683747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.683747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zkj28Ytl0fGynhQMiFKlqywC1V+VvAhuWzsMlAJ0A7+cJdF83rpyzSzeFithbq1H3G0bO8IUaQ/N1zMJapu+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.684263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4af27a9bc90fe6262cba42f38bb9dbbcbfdde0cbf9db2487102516717eae1716","sha256:cf76e54ffe6acc729ee8631e1e0100d7619d9072e433195e686b7d402a0026e3"],"state_sha256":"71750659d5e16999416552e8e6e582a65226e39dd487db6d096e310e57ac21e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KuMw/RbMW/AKmy0gVGX4JetzWn6n7F0vqIfQZ4AUPkD4BnDCKR4WetNBq1TEhYHHRI8hinJvX5cYGfA/McfDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:59:15.331355Z","bundle_sha256":"8a67a208f627dc4fd32df15045fed45e832cc9fd1d66ce1b6d18aa49e1f9ba82"}}