{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:H5C6EVBNPPD6YGCDM4AQUDO7YB","short_pith_number":"pith:H5C6EVBN","canonical_record":{"source":{"id":"1009.4405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-22T16:10:57Z","cross_cats_sorted":["math-ph","math.CV","math.MP","math.QA"],"title_canon_sha256":"78718ca60295f2f91b4f553cf3d6bf96f7dded486cd89d68862c075169fd905d","abstract_canon_sha256":"d0ee62de56dbd69ec98f6e55aa9213a24514cc0ebfa2cbc730bb00e7d4fee4a6"},"schema_version":"1.0"},"canonical_sha256":"3f45e2542d7bc7ec184367010a0ddfc07e47c6a29ac2b2822eab0256d9a073f9","source":{"kind":"arxiv","id":"1009.4405","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4405","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4405v3","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4405","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"H5C6EVBNPPD6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H5C6EVBNPPD6YGCD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H5C6EVBN","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:H5C6EVBNPPD6YGCDM4AQUDO7YB","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-22T16:10:57Z","cross_cats_sorted":["math-ph","math.CV","math.MP","math.QA"],"title_canon_sha256":"78718ca60295f2f91b4f553cf3d6bf96f7dded486cd89d68862c075169fd905d","abstract_canon_sha256":"d0ee62de56dbd69ec98f6e55aa9213a24514cc0ebfa2cbc730bb00e7d4fee4a6"},"schema_version":"1.0"},"canonical_sha256":"3f45e2542d7bc7ec184367010a0ddfc07e47c6a29ac2b2822eab0256d9a073f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:36.069096Z","signature_b64":"pqGFnYJcVeVUMSaUwvblbcwSMh4wwLxWIi8cWl2Iuq6ihrXEEObia6rMdrQ3hnhFppyWNFftU+Vuvr2GfvpKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f45e2542d7bc7ec184367010a0ddfc07e47c6a29ac2b2822eab0256d9a073f9","last_reissued_at":"2026-05-18T00:12:36.068438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:36.068438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4405","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzoWHQ6jdMx9kjDbYz9zxFSX23XMW5ELhxBk+WSRzqs39EWuTAgFZDlRwRlDDVpc9yUh6A+w0A/ZgWAUd1ukAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:07:38.797997Z"},"content_sha256":"adeef5b318759a1b927a7da321c7c106a367ee3bd2c183eeffa805a4ceea9748","schema_version":"1.0","event_id":"sha256:adeef5b318759a1b927a7da321c7c106a367ee3bd2c183eeffa805a4ceea9748"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:H5C6EVBNPPD6YGCDM4AQUDO7YB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Berezin-Toeplitz quantization on Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP","math.QA"],"primary_cat":"math.DG","authors_text":"George Marinescu, Xiaonan Ma","submitted_at":"2010-09-22T16:10:57Z","abstract_excerpt":"We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4405","kind":"arxiv","version":3},"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":"2026-05-18T00:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSB35zTRAf+99LQkOQ0j/VwP/wDMtLKPJoaw7bVCq+Y4Z977zwTFkEYG1fhuWRWA5EM6XpccYdy58ouKIuLwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:07:38.798671Z"},"content_sha256":"f2df6a783b34f85af65facf309b2995602cb6a29c8d52873a37f5094bdaf4775","schema_version":"1.0","event_id":"sha256:f2df6a783b34f85af65facf309b2995602cb6a29c8d52873a37f5094bdaf4775"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/bundle.json","state_url":"https://pith.science/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/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":"2026-06-05T06:07:38Z","links":{"resolver":"https://pith.science/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB","bundle":"https://pith.science/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/bundle.json","state":"https://pith.science/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5C6EVBNPPD6YGCDM4AQUDO7YB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H5C6EVBNPPD6YGCDM4AQUDO7YB","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":"d0ee62de56dbd69ec98f6e55aa9213a24514cc0ebfa2cbc730bb00e7d4fee4a6","cross_cats_sorted":["math-ph","math.CV","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-22T16:10:57Z","title_canon_sha256":"78718ca60295f2f91b4f553cf3d6bf96f7dded486cd89d68862c075169fd905d"},"schema_version":"1.0","source":{"id":"1009.4405","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4405","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4405v3","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4405","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"H5C6EVBNPPD6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H5C6EVBNPPD6YGCD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H5C6EVBN","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:f2df6a783b34f85af65facf309b2995602cb6a29c8d52873a37f5094bdaf4775","target":"graph","created_at":"2026-05-18T00:12:36Z","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 study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.","authors_text":"George Marinescu, Xiaonan Ma","cross_cats":["math-ph","math.CV","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-22T16:10:57Z","title":"Berezin-Toeplitz quantization on Kaehler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4405","kind":"arxiv","version":3},"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:adeef5b318759a1b927a7da321c7c106a367ee3bd2c183eeffa805a4ceea9748","target":"record","created_at":"2026-05-18T00:12:36Z","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":"d0ee62de56dbd69ec98f6e55aa9213a24514cc0ebfa2cbc730bb00e7d4fee4a6","cross_cats_sorted":["math-ph","math.CV","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-22T16:10:57Z","title_canon_sha256":"78718ca60295f2f91b4f553cf3d6bf96f7dded486cd89d68862c075169fd905d"},"schema_version":"1.0","source":{"id":"1009.4405","kind":"arxiv","version":3}},"canonical_sha256":"3f45e2542d7bc7ec184367010a0ddfc07e47c6a29ac2b2822eab0256d9a073f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f45e2542d7bc7ec184367010a0ddfc07e47c6a29ac2b2822eab0256d9a073f9","first_computed_at":"2026-05-18T00:12:36.068438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:36.068438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqGFnYJcVeVUMSaUwvblbcwSMh4wwLxWIi8cWl2Iuq6ihrXEEObia6rMdrQ3hnhFppyWNFftU+Vuvr2GfvpKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:36.069096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4405","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adeef5b318759a1b927a7da321c7c106a367ee3bd2c183eeffa805a4ceea9748","sha256:f2df6a783b34f85af65facf309b2995602cb6a29c8d52873a37f5094bdaf4775"],"state_sha256":"4ec243d4c38be5424a19529b3e9c8f1ec92bc3380081a3752702da9cb1a376b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bz0XgcYvZ7+P33nUyjImoh4V11dUHgzmYnbzB57f2X7S/HvOLh3z7wWKpc37XqrkZ4/Bpyp1XPgFjA+4UbskDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:07:38.802098Z","bundle_sha256":"34a4c273e0413ad094c762125247b14a06fafbbb98aaa7ed6eb97b83567cab97"}}