{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ZOQCXSESQYECHZNXENYLI3KSOX","short_pith_number":"pith:ZOQCXSES","canonical_record":{"source":{"id":"2303.16516","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-29T08:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"bb7da6153feec43792c6b3fd747fa4e80c338a06dddc6f8dba569cc61fbf9e51","abstract_canon_sha256":"a56ec728a1faf8d10bf16c67396cc7b5fc0f217fc1bd94bbe9672e6a9147773e"},"schema_version":"1.0"},"canonical_sha256":"cba02bc892860823e5b72370b46d5275ce8016b69ae774ddb103a94bb65460d7","source":{"kind":"arxiv","id":"2303.16516","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16516","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16516v1","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16516","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZOQCXSESQYEC","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZOQCXSESQYECHZNX","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZOQCXSES","created_at":"2026-07-05T05:56:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ZOQCXSESQYECHZNXENYLI3KSOX","target":"record","payload":{"canonical_record":{"source":{"id":"2303.16516","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-29T08:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"bb7da6153feec43792c6b3fd747fa4e80c338a06dddc6f8dba569cc61fbf9e51","abstract_canon_sha256":"a56ec728a1faf8d10bf16c67396cc7b5fc0f217fc1bd94bbe9672e6a9147773e"},"schema_version":"1.0"},"canonical_sha256":"cba02bc892860823e5b72370b46d5275ce8016b69ae774ddb103a94bb65460d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:56:07.781438Z","signature_b64":"0tH3YbtFJNLPs0rDq7UKunc0EgANJTaDd0EBzOAdtSoRlmmJYZfBOCOQ8G4ZnGmMSqANCMJjAkrizOM7LpzVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cba02bc892860823e5b72370b46d5275ce8016b69ae774ddb103a94bb65460d7","last_reissued_at":"2026-07-05T05:56:07.780928Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:56:07.780928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.16516","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":"2026-07-05T05:56:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXV7NvVI/Q3dxoHEkpxY0ubl3JUhNdWZezrp2J4KnqlxpsfGbZHmk97jBplhQ79fReDlTaqKX9c90dU6DOiRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:13:22.199757Z"},"content_sha256":"df1c4b7cc6b22692902fac4060bc3b0a841f6d0b127826b8f119709db0a0c296","schema_version":"1.0","event_id":"sha256:df1c4b7cc6b22692902fac4060bc3b0a841f6d0b127826b8f119709db0a0c296"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ZOQCXSESQYECHZNXENYLI3KSOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy stability and Milnor-Thurston invariants for Bowen-Series-like maps","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"D. Juher, F. Ma\\~nosas, J. Los, Ll. Alsed\\`a","submitted_at":"2023-03-29T08:01:24Z","abstract_excerpt":"We define a family of discontinuous maps on the circle, called Bowen-Series-like maps, for geometric presentations of surface groups. The family has $2N$ parameters, where $2N$ is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which coincides with the volume entropy of the group presentation. This approach allows a simple algorithmic computation of the volume entropy from the presentation only, using the Milnor-Thurston theory for one dimensional maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16516","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.16516/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:56:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Voa1QZdRyk/fNpiTLxWrT8NGZn7OgElpcEllrJwGbllv/o2s+vUf08b7Y5mPxNLjtLDya9gm8V7Y5s1+uRwPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:13:22.200269Z"},"content_sha256":"7ab32507554afdfbf84e3dffca7e0152a63b08f1043a124315998a7cbd1c4bd0","schema_version":"1.0","event_id":"sha256:7ab32507554afdfbf84e3dffca7e0152a63b08f1043a124315998a7cbd1c4bd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOQCXSESQYECHZNXENYLI3KSOX/bundle.json","state_url":"https://pith.science/pith/ZOQCXSESQYECHZNXENYLI3KSOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOQCXSESQYECHZNXENYLI3KSOX/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":"2026-08-04T11:13:22Z","links":{"resolver":"https://pith.science/pith/ZOQCXSESQYECHZNXENYLI3KSOX","bundle":"https://pith.science/pith/ZOQCXSESQYECHZNXENYLI3KSOX/bundle.json","state":"https://pith.science/pith/ZOQCXSESQYECHZNXENYLI3KSOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOQCXSESQYECHZNXENYLI3KSOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZOQCXSESQYECHZNXENYLI3KSOX","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":"a56ec728a1faf8d10bf16c67396cc7b5fc0f217fc1bd94bbe9672e6a9147773e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-29T08:01:24Z","title_canon_sha256":"bb7da6153feec43792c6b3fd747fa4e80c338a06dddc6f8dba569cc61fbf9e51"},"schema_version":"1.0","source":{"id":"2303.16516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16516","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16516v1","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16516","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZOQCXSESQYEC","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZOQCXSESQYECHZNX","created_at":"2026-07-05T05:56:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZOQCXSES","created_at":"2026-07-05T05:56:07Z"}],"graph_snapshots":[{"event_id":"sha256:7ab32507554afdfbf84e3dffca7e0152a63b08f1043a124315998a7cbd1c4bd0","target":"graph","created_at":"2026-07-05T05:56:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.16516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a family of discontinuous maps on the circle, called Bowen-Series-like maps, for geometric presentations of surface groups. The family has $2N$ parameters, where $2N$ is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which coincides with the volume entropy of the group presentation. This approach allows a simple algorithmic computation of the volume entropy from the presentation only, using the Milnor-Thurston theory for one dimensional maps.","authors_text":"D. Juher, F. Ma\\~nosas, J. Los, Ll. Alsed\\`a","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-29T08:01:24Z","title":"Entropy stability and Milnor-Thurston invariants for Bowen-Series-like maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16516","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:df1c4b7cc6b22692902fac4060bc3b0a841f6d0b127826b8f119709db0a0c296","target":"record","created_at":"2026-07-05T05:56:07Z","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":"a56ec728a1faf8d10bf16c67396cc7b5fc0f217fc1bd94bbe9672e6a9147773e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-29T08:01:24Z","title_canon_sha256":"bb7da6153feec43792c6b3fd747fa4e80c338a06dddc6f8dba569cc61fbf9e51"},"schema_version":"1.0","source":{"id":"2303.16516","kind":"arxiv","version":1}},"canonical_sha256":"cba02bc892860823e5b72370b46d5275ce8016b69ae774ddb103a94bb65460d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba02bc892860823e5b72370b46d5275ce8016b69ae774ddb103a94bb65460d7","first_computed_at":"2026-07-05T05:56:07.780928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:56:07.780928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tH3YbtFJNLPs0rDq7UKunc0EgANJTaDd0EBzOAdtSoRlmmJYZfBOCOQ8G4ZnGmMSqANCMJjAkrizOM7LpzVBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:56:07.781438Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.16516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df1c4b7cc6b22692902fac4060bc3b0a841f6d0b127826b8f119709db0a0c296","sha256:7ab32507554afdfbf84e3dffca7e0152a63b08f1043a124315998a7cbd1c4bd0"],"state_sha256":"f54ca1f515bd50d8c6d8c54a18fe6e4489476516b5b14f89392de92464ab2738"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTIBiKhnNoSlKz6AEshDsN+kbBBT7iFPpvMVI869dsxy7hNV/SHwjIJBJtmQtoSj42iWTThidz8YyFx+zbteAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:13:22.204303Z","bundle_sha256":"ad9d30996c5e7bb8c2d1b937ce2875afb26d50bc787cda4121ecdaccf78dbd63"}}