{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ZQITACG6UHNFHC4WMU6Y4VFJDB","short_pith_number":"pith:ZQITACG6","canonical_record":{"source":{"id":"2010.13212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-25T20:27:04Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"8c998871e825888660dde7097ad3044060143b0918e10c8b96dc5f167ed261ad","abstract_canon_sha256":"e40ee88a80be162b7b8c1a4b87313d6542cbdcac024ae1e27b5e8909df7393a0"},"schema_version":"1.0"},"canonical_sha256":"cc113008dea1da538b96653d8e54a918658e93e686a6e38df8175fcd522c8286","source":{"kind":"arxiv","id":"2010.13212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.13212","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"2010.13212v1","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.13212","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZQITACG6UHNF","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZQITACG6UHNFHC4W","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZQITACG6","created_at":"2026-07-05T01:45:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ZQITACG6UHNFHC4WMU6Y4VFJDB","target":"record","payload":{"canonical_record":{"source":{"id":"2010.13212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-25T20:27:04Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"8c998871e825888660dde7097ad3044060143b0918e10c8b96dc5f167ed261ad","abstract_canon_sha256":"e40ee88a80be162b7b8c1a4b87313d6542cbdcac024ae1e27b5e8909df7393a0"},"schema_version":"1.0"},"canonical_sha256":"cc113008dea1da538b96653d8e54a918658e93e686a6e38df8175fcd522c8286","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:45:53.036446Z","signature_b64":"C7YOk1UNLHk3Q9ocjNPyhsFPQHYE/h0k4wAP2xrkhwDC5hYfIRBh/RzvcYuC1WVGiS6Yhp7jOLhixriuLa51BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc113008dea1da538b96653d8e54a918658e93e686a6e38df8175fcd522c8286","last_reissued_at":"2026-07-05T01:45:53.036054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:45:53.036054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.13212","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":"2026-07-05T01:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M9vmKvEP8qn8SADYnEe5stIIz7BnNRlV7gXAkrTdsQPDpsAGeJN1VsH3gEUVDG+jEEIf+ntVmmAmc7e5DDIxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:27:40.750626Z"},"content_sha256":"25a9bd33be65c2d0b2bba22b97715558908bbed5e25db1c7a0cefcd8ee515879","schema_version":"1.0","event_id":"sha256:25a9bd33be65c2d0b2bba22b97715558908bbed5e25db1c7a0cefcd8ee515879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ZQITACG6UHNFHC4WMU6Y4VFJDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^{\\infty} $ norms of Husimi distributions of eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Steve Zelditch","submitted_at":"2020-10-25T20:27:04Z","abstract_excerpt":"Husimi distributions of Laplace eigenfunctions are special types of `microlocal lifts' of eigenfunctions to phase space. Their weak * limits are the well-known quantum limits or microlocal defect measures of an orthonormal basis $\\{ \\phi_j\\}$ of eigenfunctions on a Riemannian manifold $(M,g)$ . Husimi distributions are normalized mod squares of analytic continuations of eigenfunctions to the complexification of $M$, which may be identified with an open subset of the cotangent bundle $T^*M$. Husimi distributions are probability measures whose density at $\\zeta$ is the probability density of a q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.13212","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.13212/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFPTjAl/8NwDIP7sh2n4c37NzPO63KxU83lbv+IZC6a1KaWYuVBfSO3BKOUSbcctx8133lfXNoOj3VB8ybnDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:27:40.751140Z"},"content_sha256":"4171344bc526e700cd5f004b3c1c5abfe2ec096b258a3260b43a3599e5897a37","schema_version":"1.0","event_id":"sha256:4171344bc526e700cd5f004b3c1c5abfe2ec096b258a3260b43a3599e5897a37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/bundle.json","state_url":"https://pith.science/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/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":"2026-08-23T02:27:40Z","links":{"resolver":"https://pith.science/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB","bundle":"https://pith.science/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/bundle.json","state":"https://pith.science/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQITACG6UHNFHC4WMU6Y4VFJDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ZQITACG6UHNFHC4WMU6Y4VFJDB","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":"e40ee88a80be162b7b8c1a4b87313d6542cbdcac024ae1e27b5e8909df7393a0","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-25T20:27:04Z","title_canon_sha256":"8c998871e825888660dde7097ad3044060143b0918e10c8b96dc5f167ed261ad"},"schema_version":"1.0","source":{"id":"2010.13212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.13212","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"2010.13212v1","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.13212","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZQITACG6UHNF","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZQITACG6UHNFHC4W","created_at":"2026-07-05T01:45:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZQITACG6","created_at":"2026-07-05T01:45:53Z"}],"graph_snapshots":[{"event_id":"sha256:4171344bc526e700cd5f004b3c1c5abfe2ec096b258a3260b43a3599e5897a37","target":"graph","created_at":"2026-07-05T01:45:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.13212/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Husimi distributions of Laplace eigenfunctions are special types of `microlocal lifts' of eigenfunctions to phase space. Their weak * limits are the well-known quantum limits or microlocal defect measures of an orthonormal basis $\\{ \\phi_j\\}$ of eigenfunctions on a Riemannian manifold $(M,g)$ . Husimi distributions are normalized mod squares of analytic continuations of eigenfunctions to the complexification of $M$, which may be identified with an open subset of the cotangent bundle $T^*M$. Husimi distributions are probability measures whose density at $\\zeta$ is the probability density of a q","authors_text":"Steve Zelditch","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-25T20:27:04Z","title":"$L^{\\infty} $ norms of Husimi distributions of eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.13212","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":"sha256:25a9bd33be65c2d0b2bba22b97715558908bbed5e25db1c7a0cefcd8ee515879","target":"record","created_at":"2026-07-05T01:45:53Z","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":"e40ee88a80be162b7b8c1a4b87313d6542cbdcac024ae1e27b5e8909df7393a0","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-25T20:27:04Z","title_canon_sha256":"8c998871e825888660dde7097ad3044060143b0918e10c8b96dc5f167ed261ad"},"schema_version":"1.0","source":{"id":"2010.13212","kind":"arxiv","version":1}},"canonical_sha256":"cc113008dea1da538b96653d8e54a918658e93e686a6e38df8175fcd522c8286","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc113008dea1da538b96653d8e54a918658e93e686a6e38df8175fcd522c8286","first_computed_at":"2026-07-05T01:45:53.036054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:53.036054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C7YOk1UNLHk3Q9ocjNPyhsFPQHYE/h0k4wAP2xrkhwDC5hYfIRBh/RzvcYuC1WVGiS6Yhp7jOLhixriuLa51BA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:53.036446Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.13212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a9bd33be65c2d0b2bba22b97715558908bbed5e25db1c7a0cefcd8ee515879","sha256:4171344bc526e700cd5f004b3c1c5abfe2ec096b258a3260b43a3599e5897a37"],"state_sha256":"d7590185d45d3938cff33ebba5fafe7447500eb9e0120c5452d3438fe17a6059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYIVtHMnJ44JwOhP6LkN3EUCkcbf+ZcFv5hIHqos5zeRwmNS4UiQ4r93oTwGWk4cF5bv2A1uBWL8veOJSWfIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T02:27:40.756284Z","bundle_sha256":"3336201f8087fa55ef05e404a4949134d33e433cb4611a1910cba59358f744f0"}}