{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KMRC55I652YRX65DQXAHPA2UDU","short_pith_number":"pith:KMRC55I6","canonical_record":{"source":{"id":"2412.08954","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2024-12-12T05:36:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"aa40e508638fcd2156ee1ee8df7c1ecf35b923e2c687a24a8daf8a7d5ffc822f","abstract_canon_sha256":"26be1490303afbb70bd5da9cf9c81ab71c818499bd0230053927cf5fe36fe4ac"},"schema_version":"1.0"},"canonical_sha256":"53222ef51eeeb11bfba385c07783541d00528a0ddf23d13c48f06616e12ed8e9","source":{"kind":"arxiv","id":"2412.08954","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08954","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08954v2","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08954","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"KMRC55I652YR","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_16","alias_value":"KMRC55I652YRX65D","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_8","alias_value":"KMRC55I6","created_at":"2026-07-05T11:31:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KMRC55I652YRX65DQXAHPA2UDU","target":"record","payload":{"canonical_record":{"source":{"id":"2412.08954","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2024-12-12T05:36:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"aa40e508638fcd2156ee1ee8df7c1ecf35b923e2c687a24a8daf8a7d5ffc822f","abstract_canon_sha256":"26be1490303afbb70bd5da9cf9c81ab71c818499bd0230053927cf5fe36fe4ac"},"schema_version":"1.0"},"canonical_sha256":"53222ef51eeeb11bfba385c07783541d00528a0ddf23d13c48f06616e12ed8e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:42.105097Z","signature_b64":"qQtYdfgw0Vki49zmNZhVLuX/C7pY4a4xwU9RbuJj7eZo5S5IYl1c7cS1dTylnicJOfpOQ2mJ2LKed1ZhGil+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53222ef51eeeb11bfba385c07783541d00528a0ddf23d13c48f06616e12ed8e9","last_reissued_at":"2026-07-05T11:31:42.104655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:42.104655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.08954","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":"2026-07-05T11:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJStnzm+zHUlzR9++cxi7pFpcgGzUHBG8rsdqD+ob3fry0b1MRrBsfQdipJ1SJex+wSW9GH56oRdgm5zrx4BDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:38:27.990826Z"},"content_sha256":"5ca3b54b1abc7b523a1a2da5eebcbef101e874d09ad550aa7c761ba971ace458","schema_version":"1.0","event_id":"sha256:5ca3b54b1abc7b523a1a2da5eebcbef101e874d09ad550aa7c761ba971ace458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KMRC55I652YRX65DQXAHPA2UDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Informational Parsimony Perspective on Probabilistic Symmetries","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Daniel Polani, Hippolyte Charvin, Nicola Catenacci Volpi","submitted_at":"2024-12-12T05:36:14Z","abstract_excerpt":"Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce invariance extraction. Here, we formalise these arguments from a group-theoretic perspective. We then extend them to the study of more general probabilistic symmetries, through compressions preserving geometric measures of complexity. More precisely, our framework implements a trade-off between compression and preservation of the divergence from a given hierarchi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08954","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.08954/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":"2026-07-05T11:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obxjduKprXrdnI6SAkb/QJm+Dzobsd72+djWBuMY765sjA3Wxe2JAesF2UUh/IhS4DeGPAwDFnL8Xx4bj+dmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:38:27.991326Z"},"content_sha256":"6af97f71417b9ed5f6961caa470872b648fd075f9232cc6ba4cb5068bc3df127","schema_version":"1.0","event_id":"sha256:6af97f71417b9ed5f6961caa470872b648fd075f9232cc6ba4cb5068bc3df127"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMRC55I652YRX65DQXAHPA2UDU/bundle.json","state_url":"https://pith.science/pith/KMRC55I652YRX65DQXAHPA2UDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMRC55I652YRX65DQXAHPA2UDU/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":"2026-08-14T15:38:27Z","links":{"resolver":"https://pith.science/pith/KMRC55I652YRX65DQXAHPA2UDU","bundle":"https://pith.science/pith/KMRC55I652YRX65DQXAHPA2UDU/bundle.json","state":"https://pith.science/pith/KMRC55I652YRX65DQXAHPA2UDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMRC55I652YRX65DQXAHPA2UDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KMRC55I652YRX65DQXAHPA2UDU","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":"26be1490303afbb70bd5da9cf9c81ab71c818499bd0230053927cf5fe36fe4ac","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2024-12-12T05:36:14Z","title_canon_sha256":"aa40e508638fcd2156ee1ee8df7c1ecf35b923e2c687a24a8daf8a7d5ffc822f"},"schema_version":"1.0","source":{"id":"2412.08954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08954","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08954v2","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08954","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"KMRC55I652YR","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_16","alias_value":"KMRC55I652YRX65D","created_at":"2026-07-05T11:31:42Z"},{"alias_kind":"pith_short_8","alias_value":"KMRC55I6","created_at":"2026-07-05T11:31:42Z"}],"graph_snapshots":[{"event_id":"sha256:6af97f71417b9ed5f6961caa470872b648fd075f9232cc6ba4cb5068bc3df127","target":"graph","created_at":"2026-07-05T11:31:42Z","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/2412.08954/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce invariance extraction. Here, we formalise these arguments from a group-theoretic perspective. We then extend them to the study of more general probabilistic symmetries, through compressions preserving geometric measures of complexity. More precisely, our framework implements a trade-off between compression and preservation of the divergence from a given hierarchi","authors_text":"Daniel Polani, Hippolyte Charvin, Nicola Catenacci Volpi","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2024-12-12T05:36:14Z","title":"An Informational Parsimony Perspective on Probabilistic Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08954","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":"sha256:5ca3b54b1abc7b523a1a2da5eebcbef101e874d09ad550aa7c761ba971ace458","target":"record","created_at":"2026-07-05T11:31:42Z","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":"26be1490303afbb70bd5da9cf9c81ab71c818499bd0230053927cf5fe36fe4ac","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2024-12-12T05:36:14Z","title_canon_sha256":"aa40e508638fcd2156ee1ee8df7c1ecf35b923e2c687a24a8daf8a7d5ffc822f"},"schema_version":"1.0","source":{"id":"2412.08954","kind":"arxiv","version":2}},"canonical_sha256":"53222ef51eeeb11bfba385c07783541d00528a0ddf23d13c48f06616e12ed8e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53222ef51eeeb11bfba385c07783541d00528a0ddf23d13c48f06616e12ed8e9","first_computed_at":"2026-07-05T11:31:42.104655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:42.104655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qQtYdfgw0Vki49zmNZhVLuX/C7pY4a4xwU9RbuJj7eZo5S5IYl1c7cS1dTylnicJOfpOQ2mJ2LKed1ZhGil+CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:42.105097Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.08954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ca3b54b1abc7b523a1a2da5eebcbef101e874d09ad550aa7c761ba971ace458","sha256:6af97f71417b9ed5f6961caa470872b648fd075f9232cc6ba4cb5068bc3df127"],"state_sha256":"cdbc563009a33130c8a79f1b443f8c8507abfb2a5cf15edb8fa1350cc8d0c784"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aqzl3a8n9htEqOuDmxUdUiAVt/BmwK6zADHtSGmSWQtBnSEnwHoUoT65lf32QSWRP+0z+i2Yv0uWNb5uJK83AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:38:27.996416Z","bundle_sha256":"38f76fa3af5ff406db961bc54b07e8deed6e9828324905abc8463fab1569e6a5"}}