{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZC6ADMXN7HQ3CHQKTSSHAPGNLC","short_pith_number":"pith:ZC6ADMXN","canonical_record":{"source":{"id":"1410.7878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T05:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"cf8b2622860842e6b8db03a1acf7bf337fbe150ac16009838d6499670a190118","abstract_canon_sha256":"b27073ff631fe7e9c3d78fb79c538aa9ed4867361b67fdd02e1c1d88a17f4a8d"},"schema_version":"1.0"},"canonical_sha256":"c8bc01b2edf9e1b11e0a9ca4703ccd589589c2b1aa83e47d30ae1ab84c818971","source":{"kind":"arxiv","id":"1410.7878","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7878","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7878v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7878","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZC6ADMXN7HQ3","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZC6ADMXN7HQ3CHQK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZC6ADMXN","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZC6ADMXN7HQ3CHQKTSSHAPGNLC","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T05:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"cf8b2622860842e6b8db03a1acf7bf337fbe150ac16009838d6499670a190118","abstract_canon_sha256":"b27073ff631fe7e9c3d78fb79c538aa9ed4867361b67fdd02e1c1d88a17f4a8d"},"schema_version":"1.0"},"canonical_sha256":"c8bc01b2edf9e1b11e0a9ca4703ccd589589c2b1aa83e47d30ae1ab84c818971","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:07.988450Z","signature_b64":"gH0qrAFRc4++LBofdGQQkr+nKuR2wsHbUYR7gElL4etwQH2sMPhbBXGIKOtu9qiXRd6JplXncNKzXjH9xzZgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8bc01b2edf9e1b11e0a9ca4703ccd589589c2b1aa83e47d30ae1ab84c818971","last_reissued_at":"2026-05-18T02:39:07.987975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:07.987975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7878","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":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V595xxULyZBiZuWlfkKk8w2ghT5+teXc+qRMVDSKKTmhwltX78ClLS6mIZPoFlz6j0HL5MZCu4YAqkZkBX+mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:32:23.101007Z"},"content_sha256":"0f3cbf970c56840a6981f894ab5edb906bb917d10e2dd12f2a3c9a38bb574826","schema_version":"1.0","event_id":"sha256:0f3cbf970c56840a6981f894ab5edb906bb917d10e2dd12f2a3c9a38bb574826"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZC6ADMXN7HQ3CHQKTSSHAPGNLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the relation between joint and differential invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Bl\\'azquez-Sanz, Juan Sebasti\\'an D\\'iaz Arboleda","submitted_at":"2014-10-29T05:31:46Z","abstract_excerpt":"We discuss the general properties of the theory of joint invariants of a smooth Lie group action in a manifold. Many of the known results about differential invariants, including Lie's finiteness theorem, have simpler versions in the context of joint invariants. We explore the relation between joint and differential invariants, and we expose a general method that allow to compute differential invariants from joint invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7878","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":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HgAt/dKvKIolvnmSRFX+oryNZ7Cmz6E72e6IFg8v6m/o2Gjlz88e9QbSQYw7aC4CqyKk0uCR8yYeUSuJHzOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:32:23.101651Z"},"content_sha256":"7a926b36c4342ec8ab686455b4d382a0b586114b017cbe30055bd7b5d8274f73","schema_version":"1.0","event_id":"sha256:7a926b36c4342ec8ab686455b4d382a0b586114b017cbe30055bd7b5d8274f73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/bundle.json","state_url":"https://pith.science/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/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":"2026-05-30T16:32:23Z","links":{"resolver":"https://pith.science/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC","bundle":"https://pith.science/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/bundle.json","state":"https://pith.science/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZC6ADMXN7HQ3CHQKTSSHAPGNLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZC6ADMXN7HQ3CHQKTSSHAPGNLC","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":"b27073ff631fe7e9c3d78fb79c538aa9ed4867361b67fdd02e1c1d88a17f4a8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T05:31:46Z","title_canon_sha256":"cf8b2622860842e6b8db03a1acf7bf337fbe150ac16009838d6499670a190118"},"schema_version":"1.0","source":{"id":"1410.7878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7878","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7878v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7878","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZC6ADMXN7HQ3","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZC6ADMXN7HQ3CHQK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZC6ADMXN","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:7a926b36c4342ec8ab686455b4d382a0b586114b017cbe30055bd7b5d8274f73","target":"graph","created_at":"2026-05-18T02:39:07Z","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"},"paper":{"abstract_excerpt":"We discuss the general properties of the theory of joint invariants of a smooth Lie group action in a manifold. Many of the known results about differential invariants, including Lie's finiteness theorem, have simpler versions in the context of joint invariants. We explore the relation between joint and differential invariants, and we expose a general method that allow to compute differential invariants from joint invariants.","authors_text":"David Bl\\'azquez-Sanz, Juan Sebasti\\'an D\\'iaz Arboleda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T05:31:46Z","title":"A note on the relation between joint and differential invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7878","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":"sha256:0f3cbf970c56840a6981f894ab5edb906bb917d10e2dd12f2a3c9a38bb574826","target":"record","created_at":"2026-05-18T02:39:07Z","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":"b27073ff631fe7e9c3d78fb79c538aa9ed4867361b67fdd02e1c1d88a17f4a8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T05:31:46Z","title_canon_sha256":"cf8b2622860842e6b8db03a1acf7bf337fbe150ac16009838d6499670a190118"},"schema_version":"1.0","source":{"id":"1410.7878","kind":"arxiv","version":1}},"canonical_sha256":"c8bc01b2edf9e1b11e0a9ca4703ccd589589c2b1aa83e47d30ae1ab84c818971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8bc01b2edf9e1b11e0a9ca4703ccd589589c2b1aa83e47d30ae1ab84c818971","first_computed_at":"2026-05-18T02:39:07.987975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.987975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gH0qrAFRc4++LBofdGQQkr+nKuR2wsHbUYR7gElL4etwQH2sMPhbBXGIKOtu9qiXRd6JplXncNKzXjH9xzZgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.988450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f3cbf970c56840a6981f894ab5edb906bb917d10e2dd12f2a3c9a38bb574826","sha256:7a926b36c4342ec8ab686455b4d382a0b586114b017cbe30055bd7b5d8274f73"],"state_sha256":"f519e4df77470bab522daba1b459f22fc9c107f361646708d70f20ff853815f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nOOxxZb3p33+srda2rAQp5skshRQ46UHbxn2gQK1dKfnj+k0sqayiLdFDw7gVbJG45r1W38+ytuIiJqhikuCAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:32:23.105142Z","bundle_sha256":"255ab46db70d0f5acf972126931f3c243b0374e2de2c28e4e47b424036bb8eb1"}}