{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YSL64GO3E4TAAQEQ6IZZHFRT63","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":"a2cc029257074781c9abfb741c2595f57eeaf1873d6dfd0b3c44e0a6559e424e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-26T23:46:27Z","title_canon_sha256":"73be22e6d6321ed488dc9c9872004f9b409ddef67445e355ee29f551079c28b7"},"schema_version":"1.0","source":{"id":"1608.07628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07628","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07628v1","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07628","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"pith_short_12","alias_value":"YSL64GO3E4TA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YSL64GO3E4TAAQEQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YSL64GO3","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:58809a879924a8a116052d511c74da9a70c3f63c2cad405b91877799aa778fed","target":"graph","created_at":"2026-05-18T01:07:50Z","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":"Let $R^{n+1, n}$ be the vector space $R^{2n+1}$ equipped with the bilinear form $(X,Y)=X^t C_n Y$ of index $n$, where $C_n= \\sum_{i=1}^{2n+1} (-1)^{n+i-1} e_{i, 2n+2-i}$. A smooth $\\gamma: R\\to R^{n+1,n}$ is {\\it isotropic} if $\\gamma, \\gamma_x, \\ldots, \\gamma_x^{(2n)}$ are linearly independent and the span of $\\gamma, \\ldots, \\gamma_x^{(n-1)}$ is isotropic. Given an isotropic curve, we show that there is a unique up to translation parameter such that $(\\gamma_x^{(n)}, \\gamma_x^{(n)})=1$ (we call such parameter the isotropic parameter) and there also exists a natural moving frame. In this pape","authors_text":"Chuu-Lian Terng, Zhiwei Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-26T23:46:27Z","title":"Isotropic curve flows on $R^{n+1, n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07628","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:ff84e224278bb84159082368bbcabf1bb07be925618f3aa3ed9406c4c77fff0a","target":"record","created_at":"2026-05-18T01:07:50Z","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":"a2cc029257074781c9abfb741c2595f57eeaf1873d6dfd0b3c44e0a6559e424e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-26T23:46:27Z","title_canon_sha256":"73be22e6d6321ed488dc9c9872004f9b409ddef67445e355ee29f551079c28b7"},"schema_version":"1.0","source":{"id":"1608.07628","kind":"arxiv","version":1}},"canonical_sha256":"c497ee19db2726004090f233939633f6f8d7f031bc62d42ad70c5af8d4ed98ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c497ee19db2726004090f233939633f6f8d7f031bc62d42ad70c5af8d4ed98ea","first_computed_at":"2026-05-18T01:07:50.252806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:50.252806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ObRTgph9z/1w8pHue0oZg9xZWmaX+h207UsDWILjHh78W/ec/a/iJAGGiINEOdHUP3UFqNMlX3c2lCUq6Y2qBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:50.253409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff84e224278bb84159082368bbcabf1bb07be925618f3aa3ed9406c4c77fff0a","sha256:58809a879924a8a116052d511c74da9a70c3f63c2cad405b91877799aa778fed"],"state_sha256":"dec89513a67953beadd61a763824d3340dc976e514393b795554e443023bdfe7"}