{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RFOC7EIQEQYW5IHFHZBOIHH57W","short_pith_number":"pith:RFOC7EIQ","canonical_record":{"source":{"id":"1001.1515","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-10T13:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"47643f6bc8e785d6096130316a945bb11cda6944148c3ac4ad48fca9a00b6bdd","abstract_canon_sha256":"0f3bb88e7854aee6a59cb1660d4c1c061b925d5973d7852f136b42d7742a0576"},"schema_version":"1.0"},"canonical_sha256":"895c2f911024316ea0e53e42e41cfdfdade4190156f2a933457072843c075e4c","source":{"kind":"arxiv","id":"1001.1515","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1515","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1515v3","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1515","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"RFOC7EIQEQYW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RFOC7EIQEQYW5IHF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RFOC7EIQ","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RFOC7EIQEQYW5IHFHZBOIHH57W","target":"record","payload":{"canonical_record":{"source":{"id":"1001.1515","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-10T13:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"47643f6bc8e785d6096130316a945bb11cda6944148c3ac4ad48fca9a00b6bdd","abstract_canon_sha256":"0f3bb88e7854aee6a59cb1660d4c1c061b925d5973d7852f136b42d7742a0576"},"schema_version":"1.0"},"canonical_sha256":"895c2f911024316ea0e53e42e41cfdfdade4190156f2a933457072843c075e4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:48.199062Z","signature_b64":"GW7cZfqtxdmWULEED1kZmVBXq07AhzIV4VP5JcrccNlReMR0Gz/MYtz+eNOJsrexHuJlWZ5smpygUCgplwXvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"895c2f911024316ea0e53e42e41cfdfdade4190156f2a933457072843c075e4c","last_reissued_at":"2026-05-18T04:15:48.198435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:48.198435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.1515","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":"2026-05-18T04:15:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfrR1U4vw5OVEf2LHRoqwYwQgbtS8iY9qm3FJGlo4PRoe/PGwIljxm3u/0y7shIc5AN9kQPIhYnvsoPDDS7kCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:43:30.471733Z"},"content_sha256":"4178114ea75790b815024f97d973e108da9ae1d77c7471ae2c4ed091ac7a7f30","schema_version":"1.0","event_id":"sha256:4178114ea75790b815024f97d973e108da9ae1d77c7471ae2c4ed091ac7a7f30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RFOC7EIQEQYW5IHFHZBOIHH57W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular equivariant asymptotics and Weyl's law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pablo Ramacher","submitted_at":"2010-01-10T13:39:00Z","abstract_excerpt":"We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it with the reduction of the corresponding Hamiltonian flow, proving that the equivariant spectral counting function satisfies Weyl's law, together with an estimate for the remainder."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1515","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":"2026-05-18T04:15:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PP+nKLQ/208BYGfXkKxWqL2KQSkuxjzBWo/RtAPxkBK7di2cNNMe2RkOVPLbIvoQXZDCF9/uUuhnQq2yDUjeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:43:30.472079Z"},"content_sha256":"fe7b656bc021efa1122f62df259f7837b0b6156f4c416655d86d3ca33e7b8405","schema_version":"1.0","event_id":"sha256:fe7b656bc021efa1122f62df259f7837b0b6156f4c416655d86d3ca33e7b8405"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/bundle.json","state_url":"https://pith.science/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/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":"2026-06-25T05:43:30Z","links":{"resolver":"https://pith.science/pith/RFOC7EIQEQYW5IHFHZBOIHH57W","bundle":"https://pith.science/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/bundle.json","state":"https://pith.science/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFOC7EIQEQYW5IHFHZBOIHH57W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RFOC7EIQEQYW5IHFHZBOIHH57W","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":"0f3bb88e7854aee6a59cb1660d4c1c061b925d5973d7852f136b42d7742a0576","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-10T13:39:00Z","title_canon_sha256":"47643f6bc8e785d6096130316a945bb11cda6944148c3ac4ad48fca9a00b6bdd"},"schema_version":"1.0","source":{"id":"1001.1515","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1515","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1515v3","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1515","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"RFOC7EIQEQYW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RFOC7EIQEQYW5IHF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RFOC7EIQ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:fe7b656bc021efa1122f62df259f7837b0b6156f4c416655d86d3ca33e7b8405","target":"graph","created_at":"2026-05-18T04:15:48Z","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 spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it with the reduction of the corresponding Hamiltonian flow, proving that the equivariant spectral counting function satisfies Weyl's law, together with an estimate for the remainder.","authors_text":"Pablo Ramacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-10T13:39:00Z","title":"Singular equivariant asymptotics and Weyl's law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1515","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":"sha256:4178114ea75790b815024f97d973e108da9ae1d77c7471ae2c4ed091ac7a7f30","target":"record","created_at":"2026-05-18T04:15:48Z","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":"0f3bb88e7854aee6a59cb1660d4c1c061b925d5973d7852f136b42d7742a0576","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-01-10T13:39:00Z","title_canon_sha256":"47643f6bc8e785d6096130316a945bb11cda6944148c3ac4ad48fca9a00b6bdd"},"schema_version":"1.0","source":{"id":"1001.1515","kind":"arxiv","version":3}},"canonical_sha256":"895c2f911024316ea0e53e42e41cfdfdade4190156f2a933457072843c075e4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"895c2f911024316ea0e53e42e41cfdfdade4190156f2a933457072843c075e4c","first_computed_at":"2026-05-18T04:15:48.198435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:48.198435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GW7cZfqtxdmWULEED1kZmVBXq07AhzIV4VP5JcrccNlReMR0Gz/MYtz+eNOJsrexHuJlWZ5smpygUCgplwXvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:48.199062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1515","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4178114ea75790b815024f97d973e108da9ae1d77c7471ae2c4ed091ac7a7f30","sha256:fe7b656bc021efa1122f62df259f7837b0b6156f4c416655d86d3ca33e7b8405"],"state_sha256":"ea05a03a8f804a15878871c5457dd4c516398eaf9cd87e2803a9caaecb31f99c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ph+qmUJFisFj8R9s2DUTi1oozGddNghlSjvG5mfnIqUXK0sW1fIV0swARwGxnf4JI0rrZhg22EnCbRLoM0QODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:43:30.474065Z","bundle_sha256":"015a27f3aa56fab63e509b3d3f331191a2d3ed0cc8f9b6fc4524d9c2d5b93032"}}