{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:Z5UDJSU57WKVDSFC6VYHP2IFYG","short_pith_number":"pith:Z5UDJSU5","canonical_record":{"source":{"id":"math/0612547","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2006-12-19T14:30:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"888817012e0f3a785dc66444187aff8f9e933d6de1f52ab9eff3993dba478a6f","abstract_canon_sha256":"92f40e80af0174a99b7d5da2be0f9c720354519051a9e0838ac1d6791a515265"},"schema_version":"1.0"},"canonical_sha256":"cf6834ca9dfd9551c8a2f57077e905c1856fefa524879a0f4978fb1a7e7931c3","source":{"kind":"arxiv","id":"math/0612547","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612547","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612547v3","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612547","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z5UDJSU57WKV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"Z5UDJSU57WKVDSFC","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"Z5UDJSU5","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:Z5UDJSU57WKVDSFC6VYHP2IFYG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612547","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2006-12-19T14:30:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"888817012e0f3a785dc66444187aff8f9e933d6de1f52ab9eff3993dba478a6f","abstract_canon_sha256":"92f40e80af0174a99b7d5da2be0f9c720354519051a9e0838ac1d6791a515265"},"schema_version":"1.0"},"canonical_sha256":"cf6834ca9dfd9551c8a2f57077e905c1856fefa524879a0f4978fb1a7e7931c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:53.050732Z","signature_b64":"ty6K/cfY1JRA8cU/7iII0UL+evDBWIrFvqPBLLA8SXdBDY6luV2UkQBqVFiQVtw7TTuPorgOhQoRAPz1e8WYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf6834ca9dfd9551c8a2f57077e905c1856fefa524879a0f4978fb1a7e7931c3","last_reissued_at":"2026-05-18T04:08:53.049941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:53.049941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612547","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":"2026-05-18T04:08:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sNps5bh7u0Nso1sNct5jPfpQztu5U1rOwmPAwaog8XeI4qJ7ADKw3P1p6KsZtruw5W1fcn6nMHvOyuz0bhmMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:21:22.427012Z"},"content_sha256":"acbdde7ec0e271baf008afe1afd3a8f68afafc1610627ac349cd5f33f94c5b73","schema_version":"1.0","event_id":"sha256:acbdde7ec0e271baf008afe1afd3a8f68afafc1610627ac349cd5f33f94c5b73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:Z5UDJSU57WKVDSFC6VYHP2IFYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling limits for equivariant Szego kernels","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Roberto Paoletti","submitted_at":"2006-12-19T14:30:10Z","abstract_excerpt":"Suppose that the compact and connected Lie group G acts holomorphically on the irreducible complex projective manifold M, and that the action linearizes to the Hermitian ample line bundle L on M. Assume that 0 is a regular value of the associated moment map. The spaces of global holomorphic sections of powers of L may be decomposed over the finite dimensional irreducible representations of G. In this paper, we study how the holomorphic sections in each equivariant piece asymptotically concentrate along the zero locus of the moment map. In the special case where G acts freely on the zero locus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612547","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":"2026-05-18T04:08:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdqpOF3TpDTPnMe0eXFOWLfpacrXvWGQQJhcdgzuMsldo+uqIET8/H1kKWgFTaa4xCwx35VwqJpjgbRb0LW7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:21:22.427371Z"},"content_sha256":"ff24a1ffb3e3fc4d3af088a3782412c8c938f96debca882ac3aebd2ebdd84dc1","schema_version":"1.0","event_id":"sha256:ff24a1ffb3e3fc4d3af088a3782412c8c938f96debca882ac3aebd2ebdd84dc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/bundle.json","state_url":"https://pith.science/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/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":"2026-06-22T22:21:22Z","links":{"resolver":"https://pith.science/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG","bundle":"https://pith.science/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/bundle.json","state":"https://pith.science/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5UDJSU57WKVDSFC6VYHP2IFYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Z5UDJSU57WKVDSFC6VYHP2IFYG","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":"92f40e80af0174a99b7d5da2be0f9c720354519051a9e0838ac1d6791a515265","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.SG","submitted_at":"2006-12-19T14:30:10Z","title_canon_sha256":"888817012e0f3a785dc66444187aff8f9e933d6de1f52ab9eff3993dba478a6f"},"schema_version":"1.0","source":{"id":"math/0612547","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612547","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612547v3","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612547","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z5UDJSU57WKV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"Z5UDJSU57WKVDSFC","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"Z5UDJSU5","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:ff24a1ffb3e3fc4d3af088a3782412c8c938f96debca882ac3aebd2ebdd84dc1","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"Suppose that the compact and connected Lie group G acts holomorphically on the irreducible complex projective manifold M, and that the action linearizes to the Hermitian ample line bundle L on M. Assume that 0 is a regular value of the associated moment map. The spaces of global holomorphic sections of powers of L may be decomposed over the finite dimensional irreducible representations of G. In this paper, we study how the holomorphic sections in each equivariant piece asymptotically concentrate along the zero locus of the moment map. In the special case where G acts freely on the zero locus ","authors_text":"Roberto Paoletti","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2006-12-19T14:30:10Z","title":"Scaling limits for equivariant Szego kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612547","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:acbdde7ec0e271baf008afe1afd3a8f68afafc1610627ac349cd5f33f94c5b73","target":"record","created_at":"2026-05-18T04:08:53Z","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":"92f40e80af0174a99b7d5da2be0f9c720354519051a9e0838ac1d6791a515265","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.SG","submitted_at":"2006-12-19T14:30:10Z","title_canon_sha256":"888817012e0f3a785dc66444187aff8f9e933d6de1f52ab9eff3993dba478a6f"},"schema_version":"1.0","source":{"id":"math/0612547","kind":"arxiv","version":3}},"canonical_sha256":"cf6834ca9dfd9551c8a2f57077e905c1856fefa524879a0f4978fb1a7e7931c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6834ca9dfd9551c8a2f57077e905c1856fefa524879a0f4978fb1a7e7931c3","first_computed_at":"2026-05-18T04:08:53.049941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.049941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ty6K/cfY1JRA8cU/7iII0UL+evDBWIrFvqPBLLA8SXdBDY6luV2UkQBqVFiQVtw7TTuPorgOhQoRAPz1e8WYBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.050732Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612547","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acbdde7ec0e271baf008afe1afd3a8f68afafc1610627ac349cd5f33f94c5b73","sha256:ff24a1ffb3e3fc4d3af088a3782412c8c938f96debca882ac3aebd2ebdd84dc1"],"state_sha256":"e831b005d051cbfbd0c6a06805a7392a5668d0151bfb027b27176553a0c8791f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdWg2oPYlICYuwqo5mIBTuzpIiG6z15YhzC5w0z6KrAWCOj9Pko5PLOQIppdMftY9k2ZptwoLCAL96catuynDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:21:22.429265Z","bundle_sha256":"3b284800518579820592ea5275852ed3151c2405e33cf1a3df21ed304dd8807b"}}