{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DK2KYVLGLQTGTJE5ULWRTCNHXL","short_pith_number":"pith:DK2KYVLG","canonical_record":{"source":{"id":"1205.4088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-18T06:50:09Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"abeeb2d5fda1a8a57dd3bf3c314e72850eda4766bb49cbb6c0a28db6f664443b","abstract_canon_sha256":"e57ba190cfcbd69938a4fb663406abbbdc82fe10a270eeebdd70ff42a3cbe399"},"schema_version":"1.0"},"canonical_sha256":"1ab4ac55665c2669a49da2ed1989a7bad851803d44f10cc7f1369690463c1e59","source":{"kind":"arxiv","id":"1205.4088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4088","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4088v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4088","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"DK2KYVLGLQTG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DK2KYVLGLQTGTJE5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DK2KYVLG","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DK2KYVLGLQTGTJE5ULWRTCNHXL","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-18T06:50:09Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"abeeb2d5fda1a8a57dd3bf3c314e72850eda4766bb49cbb6c0a28db6f664443b","abstract_canon_sha256":"e57ba190cfcbd69938a4fb663406abbbdc82fe10a270eeebdd70ff42a3cbe399"},"schema_version":"1.0"},"canonical_sha256":"1ab4ac55665c2669a49da2ed1989a7bad851803d44f10cc7f1369690463c1e59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:22.765235Z","signature_b64":"TLAUehxdC2SDBXRNA1vLmz+SpxGK9byoCQMeheiSiaTtm6znqRFpuBDqsyoRNSrDpc5WpPhOK43WoRPEfCWZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ab4ac55665c2669a49da2ed1989a7bad851803d44f10cc7f1369690463c1e59","last_reissued_at":"2026-05-18T03:55:22.764419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:22.764419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4088","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":"2026-05-18T03:55:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86+QRKOXpEtHUUxFvRAjogxSSzcJSdL9zWu5MF8np1ujd6BHe2kH2rEIfKXz1PlqFO6Db0nSKm3MWga1f277AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:49:20.296060Z"},"content_sha256":"43954cf15d85ce89c745d1d7ce886378ccc276cf9c6c25ef1b11dc89834b3594","schema_version":"1.0","event_id":"sha256:43954cf15d85ce89c745d1d7ce886378ccc276cf9c6c25ef1b11dc89834b3594"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DK2KYVLGLQTGTJE5ULWRTCNHXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Seshadri Constants and Interpolation on Commutative Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Michael Nakamaye, St\\'ephane Fischler (LM-Orsay)","submitted_at":"2012-05-18T06:50:09Z","abstract_excerpt":"In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and vanishing theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4088","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":"2026-05-18T03:55:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RLP0cAlOBExN+Snb9eyni42wWxyicfbScBKRtAAeOjd63P4U8u1hhRVgsW3iYw7hCAxtDY6t3auD8IIOKWzcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:49:20.296419Z"},"content_sha256":"a27276ae85b133622da9471d525d1d069f1c8e0847d8e244771c17efd29c6512","schema_version":"1.0","event_id":"sha256:a27276ae85b133622da9471d525d1d069f1c8e0847d8e244771c17efd29c6512"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/bundle.json","state_url":"https://pith.science/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/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":"2026-06-25T08:49:20Z","links":{"resolver":"https://pith.science/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL","bundle":"https://pith.science/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/bundle.json","state":"https://pith.science/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DK2KYVLGLQTGTJE5ULWRTCNHXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DK2KYVLGLQTGTJE5ULWRTCNHXL","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":"e57ba190cfcbd69938a4fb663406abbbdc82fe10a270eeebdd70ff42a3cbe399","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-18T06:50:09Z","title_canon_sha256":"abeeb2d5fda1a8a57dd3bf3c314e72850eda4766bb49cbb6c0a28db6f664443b"},"schema_version":"1.0","source":{"id":"1205.4088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4088","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4088v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4088","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"DK2KYVLGLQTG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DK2KYVLGLQTGTJE5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DK2KYVLG","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:a27276ae85b133622da9471d525d1d069f1c8e0847d8e244771c17efd29c6512","target":"graph","created_at":"2026-05-18T03:55:22Z","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 study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and vanishing theorems.","authors_text":"Michael Nakamaye, St\\'ephane Fischler (LM-Orsay)","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-18T06:50:09Z","title":"Seshadri Constants and Interpolation on Commutative Algebraic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4088","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":"sha256:43954cf15d85ce89c745d1d7ce886378ccc276cf9c6c25ef1b11dc89834b3594","target":"record","created_at":"2026-05-18T03:55:22Z","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":"e57ba190cfcbd69938a4fb663406abbbdc82fe10a270eeebdd70ff42a3cbe399","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-18T06:50:09Z","title_canon_sha256":"abeeb2d5fda1a8a57dd3bf3c314e72850eda4766bb49cbb6c0a28db6f664443b"},"schema_version":"1.0","source":{"id":"1205.4088","kind":"arxiv","version":1}},"canonical_sha256":"1ab4ac55665c2669a49da2ed1989a7bad851803d44f10cc7f1369690463c1e59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ab4ac55665c2669a49da2ed1989a7bad851803d44f10cc7f1369690463c1e59","first_computed_at":"2026-05-18T03:55:22.764419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:22.764419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TLAUehxdC2SDBXRNA1vLmz+SpxGK9byoCQMeheiSiaTtm6znqRFpuBDqsyoRNSrDpc5WpPhOK43WoRPEfCWZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:22.765235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43954cf15d85ce89c745d1d7ce886378ccc276cf9c6c25ef1b11dc89834b3594","sha256:a27276ae85b133622da9471d525d1d069f1c8e0847d8e244771c17efd29c6512"],"state_sha256":"a26ec6dafae50efcd413bd6b0fbfe93055ad6ccd7561a2324f194a83b75af103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfxRFPltYZWSB9GoNVtDjR1gOVsLo+Zs7+Ys0wRfWaCgXAPl5OLnZ7eEwExZqToqCEY7KXskEeMjEEOeuqLpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:49:20.298344Z","bundle_sha256":"66ee1b72c956a98a466f155e8754b55ea9786ef99de73979efdb64b98e44a8da"}}