{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:N7YZKW2QLH2BPW5SNXB2IVEBBM","short_pith_number":"pith:N7YZKW2Q","canonical_record":{"source":{"id":"2311.17886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-29T18:38:47Z","cross_cats_sorted":["math.AG","math.PR"],"title_canon_sha256":"1b48d2bdc54355dd4fd55595c4f543dbbfb171c5232ecbee4772126bf7562d3d","abstract_canon_sha256":"01768ef156faa0ea57b3c1319608750767331d6ea55bc8edbcba76f382cda836"},"schema_version":"1.0"},"canonical_sha256":"6ff1955b5059f417dbb26dc3a454810b365535154e8a44e6583fb5c84e785a4b","source":{"kind":"arxiv","id":"2311.17886","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17886","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17886v2","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17886","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_12","alias_value":"N7YZKW2QLH2B","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"N7YZKW2QLH2BPW5S","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"N7YZKW2Q","created_at":"2026-07-05T08:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:N7YZKW2QLH2BPW5SNXB2IVEBBM","target":"record","payload":{"canonical_record":{"source":{"id":"2311.17886","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-29T18:38:47Z","cross_cats_sorted":["math.AG","math.PR"],"title_canon_sha256":"1b48d2bdc54355dd4fd55595c4f543dbbfb171c5232ecbee4772126bf7562d3d","abstract_canon_sha256":"01768ef156faa0ea57b3c1319608750767331d6ea55bc8edbcba76f382cda836"},"schema_version":"1.0"},"canonical_sha256":"6ff1955b5059f417dbb26dc3a454810b365535154e8a44e6583fb5c84e785a4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:15.987848Z","signature_b64":"QAPDB7gv6JnpfCyo6s/hYQcYVGiStNc1+rE4nm4w0GatA3+P5SHhczfIJcRn80WeawaAhWGF8wz3vuDqZng4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff1955b5059f417dbb26dc3a454810b365535154e8a44e6583fb5c84e785a4b","last_reissued_at":"2026-07-05T08:26:15.987378Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:15.987378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.17886","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":"2026-07-05T08:26:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PG/dYV2GLEY8o44xKHlX3mpGB7MrA1AuGheKn7FQwJcfIgkt4o7/ip8B8SPEtuICtrHW1vkkAQ5I5dwqlHfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:49:09.309542Z"},"content_sha256":"83b9faa06d55fecc2c23e9127c8e98f5d90675a06a3dd3edca02c54cef4fcf9f","schema_version":"1.0","event_id":"sha256:83b9faa06d55fecc2c23e9127c8e98f5d90675a06a3dd3edca02c54cef4fcf9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:N7YZKW2QLH2BPW5SNXB2IVEBBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algebraic geometry of paths via the iterated-integrals signature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.PR"],"primary_cat":"math.RA","authors_text":"Rosa Prei{\\ss}","submitted_at":"2023-11-29T18:38:47Z","abstract_excerpt":"Contrary to previous approaches bringing together algebraic geometry and signatures of paths, we introduce a Zariski topology on the space of paths itself, and study path varieties consisting of all paths whose iterated-integrals signature satisfies certain polynomial equations. Particular emphasis lies on the role of the non-associative halfshuffle, which makes it possible to describe varieties of paths that satisfy certain relations all along their trajectory. Specifically, we may understand the set of paths on a given classical algebraic variety in $\\mathbb{R}^d$ starting from a fixed point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17886","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/2311.17886/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":"2026-07-05T08:26:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doKb/4xTaHg23m9VBZCGHvjyZq7z8oaOgpZm+q2TPBoHLu4Oceem6lvezp/AIVuXRSJwTvnSk17zGOYZSA+HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:49:09.310088Z"},"content_sha256":"d1af14b12f28216329cd084451df35d58376b2e92f7406503e4a647d1d1b45ee","schema_version":"1.0","event_id":"sha256:d1af14b12f28216329cd084451df35d58376b2e92f7406503e4a647d1d1b45ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/bundle.json","state_url":"https://pith.science/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/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":"2026-08-12T18:49:09Z","links":{"resolver":"https://pith.science/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM","bundle":"https://pith.science/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/bundle.json","state":"https://pith.science/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7YZKW2QLH2BPW5SNXB2IVEBBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:N7YZKW2QLH2BPW5SNXB2IVEBBM","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":"01768ef156faa0ea57b3c1319608750767331d6ea55bc8edbcba76f382cda836","cross_cats_sorted":["math.AG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-29T18:38:47Z","title_canon_sha256":"1b48d2bdc54355dd4fd55595c4f543dbbfb171c5232ecbee4772126bf7562d3d"},"schema_version":"1.0","source":{"id":"2311.17886","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17886","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17886v2","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17886","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_12","alias_value":"N7YZKW2QLH2B","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"N7YZKW2QLH2BPW5S","created_at":"2026-07-05T08:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"N7YZKW2Q","created_at":"2026-07-05T08:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:d1af14b12f28216329cd084451df35d58376b2e92f7406503e4a647d1d1b45ee","target":"graph","created_at":"2026-07-05T08:26:15Z","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/2311.17886/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Contrary to previous approaches bringing together algebraic geometry and signatures of paths, we introduce a Zariski topology on the space of paths itself, and study path varieties consisting of all paths whose iterated-integrals signature satisfies certain polynomial equations. Particular emphasis lies on the role of the non-associative halfshuffle, which makes it possible to describe varieties of paths that satisfy certain relations all along their trajectory. Specifically, we may understand the set of paths on a given classical algebraic variety in $\\mathbb{R}^d$ starting from a fixed point","authors_text":"Rosa Prei{\\ss}","cross_cats":["math.AG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-29T18:38:47Z","title":"An algebraic geometry of paths via the iterated-integrals signature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17886","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":"sha256:83b9faa06d55fecc2c23e9127c8e98f5d90675a06a3dd3edca02c54cef4fcf9f","target":"record","created_at":"2026-07-05T08:26:15Z","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":"01768ef156faa0ea57b3c1319608750767331d6ea55bc8edbcba76f382cda836","cross_cats_sorted":["math.AG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-29T18:38:47Z","title_canon_sha256":"1b48d2bdc54355dd4fd55595c4f543dbbfb171c5232ecbee4772126bf7562d3d"},"schema_version":"1.0","source":{"id":"2311.17886","kind":"arxiv","version":2}},"canonical_sha256":"6ff1955b5059f417dbb26dc3a454810b365535154e8a44e6583fb5c84e785a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff1955b5059f417dbb26dc3a454810b365535154e8a44e6583fb5c84e785a4b","first_computed_at":"2026-07-05T08:26:15.987378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:15.987378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QAPDB7gv6JnpfCyo6s/hYQcYVGiStNc1+rE4nm4w0GatA3+P5SHhczfIJcRn80WeawaAhWGF8wz3vuDqZng4CA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:15.987848Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.17886","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83b9faa06d55fecc2c23e9127c8e98f5d90675a06a3dd3edca02c54cef4fcf9f","sha256:d1af14b12f28216329cd084451df35d58376b2e92f7406503e4a647d1d1b45ee"],"state_sha256":"e6aae977454b7033f59dad7e1cc024d292662c7229e7e42b04986f38d2440b1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvZPGVZATi9van2oQq7S/6BpEXHAk/YJmfLfhDs0oVe89XacWQRAEoswT+p5ol7e20bTv6+RH64AZJGFw02ABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T18:49:09.315383Z","bundle_sha256":"35cc601bc53d9dc2ff2dfdba90395b000084a90e2a627da7f1d524246b296aa0"}}