{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:I52ARFWQENS4N7X4ZWBQFZBPSA","short_pith_number":"pith:I52ARFWQ","canonical_record":{"source":{"id":"2607.25414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-28T08:09:49Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"eefd8a453e881205ef069fc9a831c1551441f4fa2b37ab950742d22ad6a006e3","abstract_canon_sha256":"f76e152ad188ada88fa1a557f48c9e283abc0deb3fff53ad375fe029211588eb"},"schema_version":"1.0"},"canonical_sha256":"47740896d02365c6fefccd8302e42f9020be2fc0f520330823e7c5ed357c8a9a","source":{"kind":"arxiv","id":"2607.25414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25414","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25414v1","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25414","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"I52ARFWQENS4","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"I52ARFWQENS4N7X4","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"I52ARFWQ","created_at":"2026-07-29T01:25:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:I52ARFWQENS4N7X4ZWBQFZBPSA","target":"record","payload":{"canonical_record":{"source":{"id":"2607.25414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-28T08:09:49Z","cross_cats_sorted":["math.MP","physics.class-ph"],"title_canon_sha256":"eefd8a453e881205ef069fc9a831c1551441f4fa2b37ab950742d22ad6a006e3","abstract_canon_sha256":"f76e152ad188ada88fa1a557f48c9e283abc0deb3fff53ad375fe029211588eb"},"schema_version":"1.0"},"canonical_sha256":"47740896d02365c6fefccd8302e42f9020be2fc0f520330823e7c5ed357c8a9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:25:14.439671Z","signature_b64":"lGOQmDfjp8LP9RABJ9XBJSPyu5TM99Q48z+T3TtAYexWHgtZOMvX4PZmpp+034xpcaOoT0u8336HCbVEZyUMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47740896d02365c6fefccd8302e42f9020be2fc0f520330823e7c5ed357c8a9a","last_reissued_at":"2026-07-29T01:25:14.438830Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:25:14.438830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.25414","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":"2026-07-29T01:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1w0QvgeKZeDwmIvmTewv9FC9uSw+9AjyZqduHzJnsnvY7k00t9c+/qVyP4gNJXPM/KS1kXmKpESPjbll/nfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:50:51.413770Z"},"content_sha256":"27fca2df7665429fd75f986aab2235c7a1375d354e2ade2d46cd600443cb0789","schema_version":"1.0","event_id":"sha256:27fca2df7665429fd75f986aab2235c7a1375d354e2ade2d46cd600443cb0789"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:I52ARFWQENS4N7X4ZWBQFZBPSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on a paper by F. G\\'enot and B. Brogliato on the Painlev\\'e paradox","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Stefano Pasquero","submitted_at":"2026-07-28T08:09:49Z","abstract_excerpt":"We reconsider the analysis of the Classical Painlev\\'e Problem developed by F. G\\'enot and B. Brogliato ([1] New results on Painlev\\'e paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25414","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/2607.25414/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":"2026-07-29T01:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91X0KZ3Yb1UxQXAfUCTsxzBWVXPbWXP9zSZ8fEKw9vw33/IfFNHLRnUr+m0Yyvn612iY6tmS4K4R/IAF9q+SBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:50:51.414245Z"},"content_sha256":"f10df3ad6f0e6ff6232a986bd54b19e8fc6cd57d44ef0284212eb8d9865ed215","schema_version":"1.0","event_id":"sha256:f10df3ad6f0e6ff6232a986bd54b19e8fc6cd57d44ef0284212eb8d9865ed215"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/bundle.json","state_url":"https://pith.science/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/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":"2026-08-04T08:50:51Z","links":{"resolver":"https://pith.science/pith/I52ARFWQENS4N7X4ZWBQFZBPSA","bundle":"https://pith.science/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/bundle.json","state":"https://pith.science/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I52ARFWQENS4N7X4ZWBQFZBPSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I52ARFWQENS4N7X4ZWBQFZBPSA","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":"f76e152ad188ada88fa1a557f48c9e283abc0deb3fff53ad375fe029211588eb","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-28T08:09:49Z","title_canon_sha256":"eefd8a453e881205ef069fc9a831c1551441f4fa2b37ab950742d22ad6a006e3"},"schema_version":"1.0","source":{"id":"2607.25414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25414","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25414v1","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25414","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"I52ARFWQENS4","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"I52ARFWQENS4N7X4","created_at":"2026-07-29T01:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"I52ARFWQ","created_at":"2026-07-29T01:25:14Z"}],"graph_snapshots":[{"event_id":"sha256:f10df3ad6f0e6ff6232a986bd54b19e8fc6cd57d44ef0284212eb8d9865ed215","target":"graph","created_at":"2026-07-29T01:25:14Z","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/2607.25414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We reconsider the analysis of the Classical Painlev\\'e Problem developed by F. G\\'enot and B. Brogliato ([1] New results on Painlev\\'e paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on ","authors_text":"Stefano Pasquero","cross_cats":["math.MP","physics.class-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-28T08:09:49Z","title":"Notes on a paper by F. G\\'enot and B. Brogliato on the Painlev\\'e paradox"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25414","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":"sha256:27fca2df7665429fd75f986aab2235c7a1375d354e2ade2d46cd600443cb0789","target":"record","created_at":"2026-07-29T01:25:14Z","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":"f76e152ad188ada88fa1a557f48c9e283abc0deb3fff53ad375fe029211588eb","cross_cats_sorted":["math.MP","physics.class-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math-ph","submitted_at":"2026-07-28T08:09:49Z","title_canon_sha256":"eefd8a453e881205ef069fc9a831c1551441f4fa2b37ab950742d22ad6a006e3"},"schema_version":"1.0","source":{"id":"2607.25414","kind":"arxiv","version":1}},"canonical_sha256":"47740896d02365c6fefccd8302e42f9020be2fc0f520330823e7c5ed357c8a9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47740896d02365c6fefccd8302e42f9020be2fc0f520330823e7c5ed357c8a9a","first_computed_at":"2026-07-29T01:25:14.438830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T01:25:14.438830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGOQmDfjp8LP9RABJ9XBJSPyu5TM99Q48z+T3TtAYexWHgtZOMvX4PZmpp+034xpcaOoT0u8336HCbVEZyUMAQ==","signature_status":"signed_v1","signed_at":"2026-07-29T01:25:14.439671Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27fca2df7665429fd75f986aab2235c7a1375d354e2ade2d46cd600443cb0789","sha256:f10df3ad6f0e6ff6232a986bd54b19e8fc6cd57d44ef0284212eb8d9865ed215"],"state_sha256":"b4ef82662446a20685514f0a0be899596a39f49d0c9ce91079088328461d6165"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKgK1KFB0uFZuQ8WHwFAccfualsqJ0BT2ymATiIHSdy3xkuQph97mzMSGPIou6FpUdb8HAJXeTxTLX7IBmovBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T08:50:51.417095Z","bundle_sha256":"7827f8635fb560e84013216e4a8b1894321859beaf195842223c422d33b60956"}}