{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7P6LGCRLSAO7WF6ZP3KM32AYXA","short_pith_number":"pith:7P6LGCRL","canonical_record":{"source":{"id":"1808.09312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-28T14:08:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07ce9677eb043ca3317ce6176717522c6fbec478e82b2b5e42f5592e16e38cc1","abstract_canon_sha256":"b6b2f2c67656c63251a62726cab58118e3a21ff88cf061cbe674059aa53aacdb"},"schema_version":"1.0"},"canonical_sha256":"fbfcb30a2b901dfb17d97ed4cde818b82f182fdf62918914dffa67d6c13b0e6c","source":{"kind":"arxiv","id":"1808.09312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09312","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09312v1","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09312","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"pith_short_12","alias_value":"7P6LGCRLSAO7","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7P6LGCRLSAO7WF6Z","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7P6LGCRL","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7P6LGCRLSAO7WF6ZP3KM32AYXA","target":"record","payload":{"canonical_record":{"source":{"id":"1808.09312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-28T14:08:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07ce9677eb043ca3317ce6176717522c6fbec478e82b2b5e42f5592e16e38cc1","abstract_canon_sha256":"b6b2f2c67656c63251a62726cab58118e3a21ff88cf061cbe674059aa53aacdb"},"schema_version":"1.0"},"canonical_sha256":"fbfcb30a2b901dfb17d97ed4cde818b82f182fdf62918914dffa67d6c13b0e6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:01.720478Z","signature_b64":"d8Es7i1cLkCuYakp8hSK+8DF6z0fcla+KkAQM4sE3t6CrZvYzYcchbMbvBcHLICpxu3D3s0rh0Zqujdj8PEVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbfcb30a2b901dfb17d97ed4cde818b82f182fdf62918914dffa67d6c13b0e6c","last_reissued_at":"2026-05-18T00:07:01.719763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:01.719763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.09312","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":"2026-05-18T00:07:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPlnJ5/DwzK9zbnUDewQG+SbgQwUD/YCdejvzsOIHBH01u77kLbp8l+1aO3rJd990Di2sau/ERB2ylcv/oKaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:19:19.416405Z"},"content_sha256":"1e5127d2bedf5143b65445611b69a758322339490fff0bb22bc913f79debc754","schema_version":"1.0","event_id":"sha256:1e5127d2bedf5143b65445611b69a758322339490fff0bb22bc913f79debc754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7P6LGCRLSAO7WF6ZP3KM32AYXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Immaculate line bundles on toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Anna-Lena Winz, Jaros{\\l}aw Buczy\\'nski, Klaus Altmann, Lars Kastner","submitted_at":"2018-08-28T14:08:39Z","abstract_excerpt":"We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional sequences, investigating the diagonal property, or the toric Frobenius morphism.\n  In the present paper we focus on line bundles on toric varieties. First, we present a possibility of understanding their cohomology in terms of their (generalized) momentum polytopes. Then we present a method to exhibit the entire locus of immaculate divisors within the class grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09312","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":"2026-05-18T00:07:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbPXzJtGveInr0zCOz7ONscowKfB862TM8XBNPlxX0mMaz7tUkoNgThNyEYqWrqpNHNE+cVYvTejJK+u+4G/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:19:19.416764Z"},"content_sha256":"c66424d2e279dc4cdfa198c6dffe9bfc392d1164979f6ddd2b70362abbb28bc2","schema_version":"1.0","event_id":"sha256:c66424d2e279dc4cdfa198c6dffe9bfc392d1164979f6ddd2b70362abbb28bc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/bundle.json","state_url":"https://pith.science/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/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":"2026-06-02T01:19:19Z","links":{"resolver":"https://pith.science/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA","bundle":"https://pith.science/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/bundle.json","state":"https://pith.science/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7P6LGCRLSAO7WF6ZP3KM32AYXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7P6LGCRLSAO7WF6ZP3KM32AYXA","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":"b6b2f2c67656c63251a62726cab58118e3a21ff88cf061cbe674059aa53aacdb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-28T14:08:39Z","title_canon_sha256":"07ce9677eb043ca3317ce6176717522c6fbec478e82b2b5e42f5592e16e38cc1"},"schema_version":"1.0","source":{"id":"1808.09312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09312","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09312v1","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09312","created_at":"2026-05-18T00:07:01Z"},{"alias_kind":"pith_short_12","alias_value":"7P6LGCRLSAO7","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7P6LGCRLSAO7WF6Z","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7P6LGCRL","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:c66424d2e279dc4cdfa198c6dffe9bfc392d1164979f6ddd2b70362abbb28bc2","target":"graph","created_at":"2026-05-18T00:07:01Z","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 call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional sequences, investigating the diagonal property, or the toric Frobenius morphism.\n  In the present paper we focus on line bundles on toric varieties. First, we present a possibility of understanding their cohomology in terms of their (generalized) momentum polytopes. Then we present a method to exhibit the entire locus of immaculate divisors within the class grou","authors_text":"Anna-Lena Winz, Jaros{\\l}aw Buczy\\'nski, Klaus Altmann, Lars Kastner","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-28T14:08:39Z","title":"Immaculate line bundles on toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09312","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":"sha256:1e5127d2bedf5143b65445611b69a758322339490fff0bb22bc913f79debc754","target":"record","created_at":"2026-05-18T00:07:01Z","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":"b6b2f2c67656c63251a62726cab58118e3a21ff88cf061cbe674059aa53aacdb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-28T14:08:39Z","title_canon_sha256":"07ce9677eb043ca3317ce6176717522c6fbec478e82b2b5e42f5592e16e38cc1"},"schema_version":"1.0","source":{"id":"1808.09312","kind":"arxiv","version":1}},"canonical_sha256":"fbfcb30a2b901dfb17d97ed4cde818b82f182fdf62918914dffa67d6c13b0e6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbfcb30a2b901dfb17d97ed4cde818b82f182fdf62918914dffa67d6c13b0e6c","first_computed_at":"2026-05-18T00:07:01.719763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:01.719763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d8Es7i1cLkCuYakp8hSK+8DF6z0fcla+KkAQM4sE3t6CrZvYzYcchbMbvBcHLICpxu3D3s0rh0Zqujdj8PEVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:01.720478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e5127d2bedf5143b65445611b69a758322339490fff0bb22bc913f79debc754","sha256:c66424d2e279dc4cdfa198c6dffe9bfc392d1164979f6ddd2b70362abbb28bc2"],"state_sha256":"1b67c3017083d515a8f15c7d3c445bddfc73647e651ac0fea3401084ef479792"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OubZYa/YNpvu/wJSaiP8E5clXY1Wxvd8sXxmqQELMFqKhbo7ci/D1FTQSkOGUpVFkUwRz+9uhECONVRYmdTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:19:19.418768Z","bundle_sha256":"f1382f274bc91e10accc8ce0430d3e194e58a4eff07e577d8232e1fc0ea26bd7"}}