{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6I7UZSRUOMPVTNLFMPZFCR2BBW","short_pith_number":"pith:6I7UZSRU","canonical_record":{"source":{"id":"1907.08423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-19T09:26:37Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"64954c5338a2900cada2b672cb8bf380d704509e6894b8cfcad43d70b9094e87","abstract_canon_sha256":"59d8cebd728c27dece6ef029254e5695a3a01c4e6c3ea91a2725806445a83d40"},"schema_version":"1.0"},"canonical_sha256":"f23f4cca34731f59b56563f25147410da2a5875fa3597882fb395e9c05d538cf","source":{"kind":"arxiv","id":"1907.08423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08423","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08423v1","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08423","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"6I7UZSRUOMPV","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6I7UZSRUOMPVTNLF","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6I7UZSRU","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6I7UZSRUOMPVTNLFMPZFCR2BBW","target":"record","payload":{"canonical_record":{"source":{"id":"1907.08423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-19T09:26:37Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"64954c5338a2900cada2b672cb8bf380d704509e6894b8cfcad43d70b9094e87","abstract_canon_sha256":"59d8cebd728c27dece6ef029254e5695a3a01c4e6c3ea91a2725806445a83d40"},"schema_version":"1.0"},"canonical_sha256":"f23f4cca34731f59b56563f25147410da2a5875fa3597882fb395e9c05d538cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:09.903981Z","signature_b64":"b2wfvhI+JbbtGmW4OCBlXk8IqT6hMS4JIzwnHizbyKOVG8dw9m46xGHJWLN1KLOBzijN6CFkbQhBX8CpMzpUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f23f4cca34731f59b56563f25147410da2a5875fa3597882fb395e9c05d538cf","last_reissued_at":"2026-05-17T23:40:09.903494Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:09.903494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.08423","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":"2026-05-17T23:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xPq9kKLtUlTo8CIFBPLS4vYl/GNkesGvKXvNvNu0RVl6AH60TBkSuDqAO8Ib/ZySqchxHD+dCgpY9hiXl3BCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:51:45.207937Z"},"content_sha256":"990f160397ed841c2068964f1880318b4c483b8daeece49182cefd29349a49bd","schema_version":"1.0","event_id":"sha256:990f160397ed841c2068964f1880318b4c483b8daeece49182cefd29349a49bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6I7UZSRUOMPVTNLFMPZFCR2BBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Insertion algorithm for inverting the signature of a path","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Jiawei Chang, Terry Lyons","submitted_at":"2019-07-19T09:26:37Z","abstract_excerpt":"In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the inserted n-th term and the (n+1)-th term of the normalised signature of a smooth path, and we also show that there exists a constant lower bound for a subsequence of the terms in the normalised signature of a piecewise linear path. We demonstrate our results with numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08423","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":"2026-05-17T23:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXUsELAIdUuO2EgBfzM7FZTddyQw4F0/p1uNfeQr6Vn6FRxUOo662Sp6TUDxyZs+cTm/TBfy8w4CELYiMgemAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:51:45.208277Z"},"content_sha256":"593afbd11d00e4b26bdf2d11b140ae425f721d1076ee4ea76b03c2690c7806bd","schema_version":"1.0","event_id":"sha256:593afbd11d00e4b26bdf2d11b140ae425f721d1076ee4ea76b03c2690c7806bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/bundle.json","state_url":"https://pith.science/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/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":"2026-05-19T11:51:45Z","links":{"resolver":"https://pith.science/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW","bundle":"https://pith.science/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/bundle.json","state":"https://pith.science/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6I7UZSRUOMPVTNLFMPZFCR2BBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6I7UZSRUOMPVTNLFMPZFCR2BBW","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":"59d8cebd728c27dece6ef029254e5695a3a01c4e6c3ea91a2725806445a83d40","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-19T09:26:37Z","title_canon_sha256":"64954c5338a2900cada2b672cb8bf380d704509e6894b8cfcad43d70b9094e87"},"schema_version":"1.0","source":{"id":"1907.08423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08423","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08423v1","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08423","created_at":"2026-05-17T23:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"6I7UZSRUOMPV","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6I7UZSRUOMPVTNLF","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6I7UZSRU","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:593afbd11d00e4b26bdf2d11b140ae425f721d1076ee4ea76b03c2690c7806bd","target":"graph","created_at":"2026-05-17T23:40:09Z","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 article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the inserted n-th term and the (n+1)-th term of the normalised signature of a smooth path, and we also show that there exists a constant lower bound for a subsequence of the terms in the normalised signature of a piecewise linear path. We demonstrate our results with numerical examples.","authors_text":"Jiawei Chang, Terry Lyons","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-19T09:26:37Z","title":"Insertion algorithm for inverting the signature of a path"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08423","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":"sha256:990f160397ed841c2068964f1880318b4c483b8daeece49182cefd29349a49bd","target":"record","created_at":"2026-05-17T23:40:09Z","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":"59d8cebd728c27dece6ef029254e5695a3a01c4e6c3ea91a2725806445a83d40","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-19T09:26:37Z","title_canon_sha256":"64954c5338a2900cada2b672cb8bf380d704509e6894b8cfcad43d70b9094e87"},"schema_version":"1.0","source":{"id":"1907.08423","kind":"arxiv","version":1}},"canonical_sha256":"f23f4cca34731f59b56563f25147410da2a5875fa3597882fb395e9c05d538cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f23f4cca34731f59b56563f25147410da2a5875fa3597882fb395e9c05d538cf","first_computed_at":"2026-05-17T23:40:09.903494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:09.903494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b2wfvhI+JbbtGmW4OCBlXk8IqT6hMS4JIzwnHizbyKOVG8dw9m46xGHJWLN1KLOBzijN6CFkbQhBX8CpMzpUDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:09.903981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:990f160397ed841c2068964f1880318b4c483b8daeece49182cefd29349a49bd","sha256:593afbd11d00e4b26bdf2d11b140ae425f721d1076ee4ea76b03c2690c7806bd"],"state_sha256":"340d8c1d6ded6147bc97df7e4074e966e727218ccc5fe4823903dca12a7dd13d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+CWdIomBGQzx5zvy/2QXgSZvveKVOEZndYRsZVNxe4TvZ5W6fAKYeLXiwhvegaIGAMu5Vg6k+YEAKcFiVgnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T11:51:45.209845Z","bundle_sha256":"5614053b912c1da1b755fad528523a75cb939d1a8029c04a04655d8ecbfa792d"}}