{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:HMDVGUDE7TSR6QC6GMLMAYRLZI","short_pith_number":"pith:HMDVGUDE","canonical_record":{"source":{"id":"0903.3471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-20T09:46:12Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"7b71eeb600fafdd65f4119a67abf5e0acab621438b6f497d3aac8d7d2a79a06e","abstract_canon_sha256":"49b982559818e84f9dfcfdf25bfe98d01425cb7ec1c7a79f2e8495dd8fb8539f"},"schema_version":"1.0"},"canonical_sha256":"3b07535064fce51f405e3316c0622bca2bacecf432a52fb663cf05bcca00d4fd","source":{"kind":"arxiv","id":"0903.3471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3471","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3471v1","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3471","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"HMDVGUDE7TSR","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HMDVGUDE7TSR6QC6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HMDVGUDE","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:HMDVGUDE7TSR6QC6GMLMAYRLZI","target":"record","payload":{"canonical_record":{"source":{"id":"0903.3471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-20T09:46:12Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"7b71eeb600fafdd65f4119a67abf5e0acab621438b6f497d3aac8d7d2a79a06e","abstract_canon_sha256":"49b982559818e84f9dfcfdf25bfe98d01425cb7ec1c7a79f2e8495dd8fb8539f"},"schema_version":"1.0"},"canonical_sha256":"3b07535064fce51f405e3316c0622bca2bacecf432a52fb663cf05bcca00d4fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:05.588461Z","signature_b64":"MtIerme7Nv8L84QFq6IjG9CB+4IhQpmTGfXoyW9P5J68CiWpTSOTuTUBqlS00DFCRO9etyVmUUqz/KOMNxyPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b07535064fce51f405e3316c0622bca2bacecf432a52fb663cf05bcca00d4fd","last_reissued_at":"2026-05-18T00:18:05.587857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:05.587857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.3471","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/AgV3dyVFpefg4Gse4Jn2ubnU78QU0eAImdDtQ50aaR5/0GNg8C2l5D8TLNfcq2V37/DwzbWx++J8eBTgcUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:35:09.718974Z"},"content_sha256":"dcfe0b4ab5e366ebabf545043a4d3025176dde644daa903dddac53b85fae0695","schema_version":"1.0","event_id":"sha256:dcfe0b4ab5e366ebabf545043a4d3025176dde644daa903dddac53b85fae0695"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:HMDVGUDE7TSR6QC6GMLMAYRLZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Jacobian of the harmonic moment map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CV","authors_text":"Bj\\\"orn Gustafsson, Vladimir G. Tkachev","submitted_at":"2009-03-20T09:46:12Z","abstract_excerpt":"In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic moment map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3471","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILTshGNkHQcoAWBMfw2MmLw3TtjrN0TzVImcF8llyTCLjHF0Z216U/y0VSkTEQbocdjpAr3cmc8WhPeeJBdCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:35:09.719338Z"},"content_sha256":"ae383045240999528f245d8f36c65e7a239c0dbacd6a131620491735d92bbc59","schema_version":"1.0","event_id":"sha256:ae383045240999528f245d8f36c65e7a239c0dbacd6a131620491735d92bbc59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/bundle.json","state_url":"https://pith.science/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/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":"2026-06-03T08:35:09Z","links":{"resolver":"https://pith.science/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI","bundle":"https://pith.science/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/bundle.json","state":"https://pith.science/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMDVGUDE7TSR6QC6GMLMAYRLZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HMDVGUDE7TSR6QC6GMLMAYRLZI","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":"49b982559818e84f9dfcfdf25bfe98d01425cb7ec1c7a79f2e8495dd8fb8539f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-20T09:46:12Z","title_canon_sha256":"7b71eeb600fafdd65f4119a67abf5e0acab621438b6f497d3aac8d7d2a79a06e"},"schema_version":"1.0","source":{"id":"0903.3471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3471","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3471v1","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3471","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"HMDVGUDE7TSR","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HMDVGUDE7TSR6QC6","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HMDVGUDE","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:ae383045240999528f245d8f36c65e7a239c0dbacd6a131620491735d92bbc59","target":"graph","created_at":"2026-05-18T00:18:05Z","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":"In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic moment map.","authors_text":"Bj\\\"orn Gustafsson, Vladimir G. Tkachev","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-20T09:46:12Z","title":"On the Jacobian of the harmonic moment map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3471","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:dcfe0b4ab5e366ebabf545043a4d3025176dde644daa903dddac53b85fae0695","target":"record","created_at":"2026-05-18T00:18:05Z","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":"49b982559818e84f9dfcfdf25bfe98d01425cb7ec1c7a79f2e8495dd8fb8539f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-20T09:46:12Z","title_canon_sha256":"7b71eeb600fafdd65f4119a67abf5e0acab621438b6f497d3aac8d7d2a79a06e"},"schema_version":"1.0","source":{"id":"0903.3471","kind":"arxiv","version":1}},"canonical_sha256":"3b07535064fce51f405e3316c0622bca2bacecf432a52fb663cf05bcca00d4fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b07535064fce51f405e3316c0622bca2bacecf432a52fb663cf05bcca00d4fd","first_computed_at":"2026-05-18T00:18:05.587857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.587857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MtIerme7Nv8L84QFq6IjG9CB+4IhQpmTGfXoyW9P5J68CiWpTSOTuTUBqlS00DFCRO9etyVmUUqz/KOMNxyPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.588461Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcfe0b4ab5e366ebabf545043a4d3025176dde644daa903dddac53b85fae0695","sha256:ae383045240999528f245d8f36c65e7a239c0dbacd6a131620491735d92bbc59"],"state_sha256":"91bc7c03b32c3a0f641ed97807ecdb8a4091132e64ffc016c54ab05ee7d3f13d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyzj1dulsbBZuGPYTORKC1n/x3gVK2ItCFn6UkxqstmyePd7Ecp1zVrczsyx2poVB0uWnSDr27np2YKsUb0TAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:35:09.721260Z","bundle_sha256":"eff11ab2abcf013cd9758e0f45c7fe9255ae409d54efca2cb854d1036c80b60c"}}