{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HD2PLOWAXQ4TL3QKYRKRT34OV3","short_pith_number":"pith:HD2PLOWA","canonical_record":{"source":{"id":"1404.4892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-18T21:35:56Z","cross_cats_sorted":[],"title_canon_sha256":"09e83f9ef0a5ad30e5398f77ea5192479491ce50b36cbace041a4d80eda4cdca","abstract_canon_sha256":"d2b9924fa2b7ec026d21a2d4f4006ac3789144abaf5936572236c17ffdb0d76b"},"schema_version":"1.0"},"canonical_sha256":"38f4f5bac0bc3935ee0ac45519ef8eaed4f03a4bf9dde1280404975f669a0436","source":{"kind":"arxiv","id":"1404.4892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4892","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4892v2","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4892","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"HD2PLOWAXQ4T","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HD2PLOWAXQ4TL3QK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HD2PLOWA","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HD2PLOWAXQ4TL3QKYRKRT34OV3","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-18T21:35:56Z","cross_cats_sorted":[],"title_canon_sha256":"09e83f9ef0a5ad30e5398f77ea5192479491ce50b36cbace041a4d80eda4cdca","abstract_canon_sha256":"d2b9924fa2b7ec026d21a2d4f4006ac3789144abaf5936572236c17ffdb0d76b"},"schema_version":"1.0"},"canonical_sha256":"38f4f5bac0bc3935ee0ac45519ef8eaed4f03a4bf9dde1280404975f669a0436","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.218734Z","signature_b64":"X6UqiAh6Fjw2KkqpYhAdAIyEpIADIDZ50IFBWo1Uk/5s6TXpewbGiihsJfaeq6ujqu6AhSVuuwtVcjvSAxQoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38f4f5bac0bc3935ee0ac45519ef8eaed4f03a4bf9dde1280404975f669a0436","last_reissued_at":"2026-05-18T01:35:05.218043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.218043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4892","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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOQI7E6Uyg1WA8DjW+lMsBM8hT/Qq5XmOVYUi5vWy1nly+SslExyzxLz0gFkWxbnK2aLyIZYT+FHDhlfzVe2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:12:00.590193Z"},"content_sha256":"25371638c5ec09c38b4dd606e1d3d2d47c7dc4a7d15c5241d52e84d207da0549","schema_version":"1.0","event_id":"sha256:25371638c5ec09c38b4dd606e1d3d2d47c7dc4a7d15c5241d52e84d207da0549"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HD2PLOWAXQ4TL3QKYRKRT34OV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolation and vector bundles on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atanas Atanasov","submitted_at":"2014-04-18T21:35:56Z","abstract_excerpt":"We define several notions of interpolation for vector bundles on curves and discuss their relation to slope stability. The heart of the paper demonstrates how to use degeneration arguments to prove interpolation. We use these ideas to show that a general connected space curve of degree $d$ and genus $g$ satisfies interpolation for $d \\geq g+3$ unless $d = 5$ and $g = 2$. As a second application, we show that a general elliptic curve of degree $d$ in $\\mathbb{P}^n$ satisfies weak interpolation when $d \\geq 7$, $d \\geq n+1$, and the remainder of $2d$ modulo $n-1$ lies between $3$ and $n-2$ inclu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4892","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":""},"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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tr0Xsp6Gx6uwr74dmP8zVcSFrrI4xvmlAYyXhtD8H5lsOzCmEFTOja9XyeQCdrsva5hXwwjD3KzCmRNMZVT1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:12:00.590884Z"},"content_sha256":"329e5a997cb430f6a22fac8e8a6ccf40b0987fddcc70e1613e8dbabc5b068691","schema_version":"1.0","event_id":"sha256:329e5a997cb430f6a22fac8e8a6ccf40b0987fddcc70e1613e8dbabc5b068691"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/bundle.json","state_url":"https://pith.science/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/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":"2026-06-07T16:12:00Z","links":{"resolver":"https://pith.science/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3","bundle":"https://pith.science/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/bundle.json","state":"https://pith.science/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HD2PLOWAXQ4TL3QKYRKRT34OV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HD2PLOWAXQ4TL3QKYRKRT34OV3","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":"d2b9924fa2b7ec026d21a2d4f4006ac3789144abaf5936572236c17ffdb0d76b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-18T21:35:56Z","title_canon_sha256":"09e83f9ef0a5ad30e5398f77ea5192479491ce50b36cbace041a4d80eda4cdca"},"schema_version":"1.0","source":{"id":"1404.4892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4892","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4892v2","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4892","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"HD2PLOWAXQ4T","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HD2PLOWAXQ4TL3QK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HD2PLOWA","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:329e5a997cb430f6a22fac8e8a6ccf40b0987fddcc70e1613e8dbabc5b068691","target":"graph","created_at":"2026-05-18T01:35:05Z","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":"We define several notions of interpolation for vector bundles on curves and discuss their relation to slope stability. The heart of the paper demonstrates how to use degeneration arguments to prove interpolation. We use these ideas to show that a general connected space curve of degree $d$ and genus $g$ satisfies interpolation for $d \\geq g+3$ unless $d = 5$ and $g = 2$. As a second application, we show that a general elliptic curve of degree $d$ in $\\mathbb{P}^n$ satisfies weak interpolation when $d \\geq 7$, $d \\geq n+1$, and the remainder of $2d$ modulo $n-1$ lies between $3$ and $n-2$ inclu","authors_text":"Atanas Atanasov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-18T21:35:56Z","title":"Interpolation and vector bundles on curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4892","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":"sha256:25371638c5ec09c38b4dd606e1d3d2d47c7dc4a7d15c5241d52e84d207da0549","target":"record","created_at":"2026-05-18T01:35:05Z","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":"d2b9924fa2b7ec026d21a2d4f4006ac3789144abaf5936572236c17ffdb0d76b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-18T21:35:56Z","title_canon_sha256":"09e83f9ef0a5ad30e5398f77ea5192479491ce50b36cbace041a4d80eda4cdca"},"schema_version":"1.0","source":{"id":"1404.4892","kind":"arxiv","version":2}},"canonical_sha256":"38f4f5bac0bc3935ee0ac45519ef8eaed4f03a4bf9dde1280404975f669a0436","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38f4f5bac0bc3935ee0ac45519ef8eaed4f03a4bf9dde1280404975f669a0436","first_computed_at":"2026-05-18T01:35:05.218043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:05.218043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X6UqiAh6Fjw2KkqpYhAdAIyEpIADIDZ50IFBWo1Uk/5s6TXpewbGiihsJfaeq6ujqu6AhSVuuwtVcjvSAxQoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:05.218734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25371638c5ec09c38b4dd606e1d3d2d47c7dc4a7d15c5241d52e84d207da0549","sha256:329e5a997cb430f6a22fac8e8a6ccf40b0987fddcc70e1613e8dbabc5b068691"],"state_sha256":"a3077b0a63243ebabd60b2fe0dac38432b5d665a7d6a754519797b5933d330ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6EWbavAuZw+Gen4VOVPPpmfx11keJgRrMYqm8SCqIizsRQBS2csVqkyaFtdsEBHvJX7r5ocr+3afVfHkg58/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:12:00.594627Z","bundle_sha256":"276c50e141c684ed6882db0e267d565b3778067c8a559929dfa5118134e45cf9"}}