{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:73O2DA6AIJ2EKAXDBJDGLB6O5V","short_pith_number":"pith:73O2DA6A","canonical_record":{"source":{"id":"2111.02466","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-11-03T18:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"023abb095a0ecc3fe87095542ca7cc3d621a883cd501364ffcd92c0adbea5140","abstract_canon_sha256":"225f7047e1a2c5b7e5d932049b8f0c8c5b644d72ec56799a40e81311c1bee6a8"},"schema_version":"1.0"},"canonical_sha256":"fedda183c042744502e30a466587ceed7691d52c759dc83fe515b78184119d5b","source":{"kind":"arxiv","id":"2111.02466","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.02466","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"arxiv_version","alias_value":"2111.02466v1","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.02466","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_12","alias_value":"73O2DA6AIJ2E","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_16","alias_value":"73O2DA6AIJ2EKAXD","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_8","alias_value":"73O2DA6A","created_at":"2026-07-05T03:28:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:73O2DA6AIJ2EKAXDBJDGLB6O5V","target":"record","payload":{"canonical_record":{"source":{"id":"2111.02466","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-11-03T18:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"023abb095a0ecc3fe87095542ca7cc3d621a883cd501364ffcd92c0adbea5140","abstract_canon_sha256":"225f7047e1a2c5b7e5d932049b8f0c8c5b644d72ec56799a40e81311c1bee6a8"},"schema_version":"1.0"},"canonical_sha256":"fedda183c042744502e30a466587ceed7691d52c759dc83fe515b78184119d5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:28:51.856795Z","signature_b64":"Bh2K2Ju+ra5uaVzmHKGX82hkmF9Av9yGqHymdftP2kyAWJMWg8URRjjc+ZyZOGuIFFT1OJVsjeD65QLL10PoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fedda183c042744502e30a466587ceed7691d52c759dc83fe515b78184119d5b","last_reissued_at":"2026-07-05T03:28:51.856386Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:28:51.856386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.02466","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":"2026-07-05T03:28:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DlNdvShjHIXkF35zVJR+TeZbUZKfyXh35tZ3Ty5wOz29BHfBCPb/Rn/INf256ZvgqteZDgEOLZsFsvlJUGO7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:59:50.010857Z"},"content_sha256":"c9f195fc3b74824506a508155c0a7f49eee6d622b971e719f64cfd5be3f34243","schema_version":"1.0","event_id":"sha256:c9f195fc3b74824506a508155c0a7f49eee6d622b971e719f64cfd5be3f34243"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:73O2DA6AIJ2EKAXDBJDGLB6O5V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolation of rational scrolls","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ziv Ran","submitted_at":"2021-11-03T18:42:32Z","abstract_excerpt":"We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in $\\P^{2k+1}$ for all $m\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02466","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.02466/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":"2026-07-05T03:28:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oe2C5wsmmxIFYjy2PCcZFCtDWmPH0+aYrC5qxk2hxF0u/ObuvgZmkRqG4CG1+xMggF1FlLdaldE1HH86QFr/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:59:50.011219Z"},"content_sha256":"bdfbf54d41c7569f051857c31178e166136e8b7b3a2c2afae5553f052ff66571","schema_version":"1.0","event_id":"sha256:bdfbf54d41c7569f051857c31178e166136e8b7b3a2c2afae5553f052ff66571"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/bundle.json","state_url":"https://pith.science/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/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":"2026-07-07T13:59:50Z","links":{"resolver":"https://pith.science/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V","bundle":"https://pith.science/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/bundle.json","state":"https://pith.science/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73O2DA6AIJ2EKAXDBJDGLB6O5V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:73O2DA6AIJ2EKAXDBJDGLB6O5V","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":"225f7047e1a2c5b7e5d932049b8f0c8c5b644d72ec56799a40e81311c1bee6a8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-11-03T18:42:32Z","title_canon_sha256":"023abb095a0ecc3fe87095542ca7cc3d621a883cd501364ffcd92c0adbea5140"},"schema_version":"1.0","source":{"id":"2111.02466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.02466","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"arxiv_version","alias_value":"2111.02466v1","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.02466","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_12","alias_value":"73O2DA6AIJ2E","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_16","alias_value":"73O2DA6AIJ2EKAXD","created_at":"2026-07-05T03:28:51Z"},{"alias_kind":"pith_short_8","alias_value":"73O2DA6A","created_at":"2026-07-05T03:28:51Z"}],"graph_snapshots":[{"event_id":"sha256:bdfbf54d41c7569f051857c31178e166136e8b7b3a2c2afae5553f052ff66571","target":"graph","created_at":"2026-07-05T03:28:51Z","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/2111.02466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in $\\P^{2k+1}$ for all $m\\geq 1$.","authors_text":"Ziv Ran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-11-03T18:42:32Z","title":"Interpolation of rational scrolls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02466","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:c9f195fc3b74824506a508155c0a7f49eee6d622b971e719f64cfd5be3f34243","target":"record","created_at":"2026-07-05T03:28:51Z","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":"225f7047e1a2c5b7e5d932049b8f0c8c5b644d72ec56799a40e81311c1bee6a8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-11-03T18:42:32Z","title_canon_sha256":"023abb095a0ecc3fe87095542ca7cc3d621a883cd501364ffcd92c0adbea5140"},"schema_version":"1.0","source":{"id":"2111.02466","kind":"arxiv","version":1}},"canonical_sha256":"fedda183c042744502e30a466587ceed7691d52c759dc83fe515b78184119d5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fedda183c042744502e30a466587ceed7691d52c759dc83fe515b78184119d5b","first_computed_at":"2026-07-05T03:28:51.856386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:28:51.856386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bh2K2Ju+ra5uaVzmHKGX82hkmF9Av9yGqHymdftP2kyAWJMWg8URRjjc+ZyZOGuIFFT1OJVsjeD65QLL10PoAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:28:51.856795Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.02466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9f195fc3b74824506a508155c0a7f49eee6d622b971e719f64cfd5be3f34243","sha256:bdfbf54d41c7569f051857c31178e166136e8b7b3a2c2afae5553f052ff66571"],"state_sha256":"72d462c29585211d846a69a9255ff601f64a5f977dc598a8c82befd9bdd857ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPhTeGE1GlJuP2vSSQtxJyK9R7TINO/Ak7HniPYM/yPsV6Se/Yei5mpv6p+JqxbX89p7XXHDFIN2DPb97wttBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:59:50.013586Z","bundle_sha256":"516830b17240a32c58632f5cd34ce1b89ffc4c4bd64460e6e14631fb632854bd"}}