{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:W442TR7LXXP6DTPEB4TCA2EHAH","short_pith_number":"pith:W442TR7L","canonical_record":{"source":{"id":"1204.1305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T18:50:55Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"bda462533ed3bf48db238e785ccd061235817184d46478c5c0e69e07629d0083","abstract_canon_sha256":"672aa67f5e591ffe276bf4f3a7b46247a1bc95bf6724ad3cac09241b8067b863"},"schema_version":"1.0"},"canonical_sha256":"b739a9c7ebbddfe1cde40f2620688701f4b06913b208ad1c67190c171ccba2e0","source":{"kind":"arxiv","id":"1204.1305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1305","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1305v2","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1305","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"W442TR7LXXP6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W442TR7LXXP6DTPE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W442TR7L","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:W442TR7LXXP6DTPEB4TCA2EHAH","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T18:50:55Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"bda462533ed3bf48db238e785ccd061235817184d46478c5c0e69e07629d0083","abstract_canon_sha256":"672aa67f5e591ffe276bf4f3a7b46247a1bc95bf6724ad3cac09241b8067b863"},"schema_version":"1.0"},"canonical_sha256":"b739a9c7ebbddfe1cde40f2620688701f4b06913b208ad1c67190c171ccba2e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.029533Z","signature_b64":"GiEKdY55G1050MA7r1N0UwNVqy778oNkYb7uaBDDB6RGSbtXSoVSmKmhiHeVKogrEfYgBYgIzrkVtv87UP8JAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b739a9c7ebbddfe1cde40f2620688701f4b06913b208ad1c67190c171ccba2e0","last_reissued_at":"2026-05-18T02:20:48.028786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.028786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1305","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHoMujDSfvvWiLWLk/aQ5Bghc5C47u1rBeJt1Kv942cwRY+XlInnfvO8OeGC/48StwXPzXAURR1xBN/aGbGtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:57:22.086922Z"},"content_sha256":"eb4f161fe365dd419c8bc77e94a81f8c9ab7dd24a8eba662ada3049ddedbae5b","schema_version":"1.0","event_id":"sha256:eb4f161fe365dd419c8bc77e94a81f8c9ab7dd24a8eba662ada3049ddedbae5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:W442TR7LXXP6DTPEB4TCA2EHAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Microlocal limits of plane waves and Eisenstein functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Colin Guillarmou, Semyon Dyatlov","submitted_at":"2012-04-05T18:50:55Z","abstract_excerpt":"We study microlocal limits of plane waves on noncompact Riemannian manifolds (M,g) which are either Euclidean or asymptotically hyperbolic with curvature -1 near infinity. The plane waves E(z,\\xi) are functions on M parametrized by the square root of energy z and the direction of the wave, \\xi, interpreted as a point at infinity. If the trapped set K for the geodesic flow has Liouville measure zero, we show that, as z\\to +\\infty, E(z,\\xi) microlocally converges to a measure \\mu_\\xi, in average on energy intervals of fixed size, [z,z+1], and in \\xi. We express the rate of convergence to the lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1305","kind":"arxiv","version":2},"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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LO0JmOjGuDciAbLuin3G8f541ia781D3tJktOuoulWWMYDc2iNrQCJkEabt1Zv7OuA3GdZUD0byeTOyNz5fADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:57:22.087596Z"},"content_sha256":"f1865ccd5bbae58e4d44c4a3d31857bf10196b5d20a999d0bcfe5e4cab123ddb","schema_version":"1.0","event_id":"sha256:f1865ccd5bbae58e4d44c4a3d31857bf10196b5d20a999d0bcfe5e4cab123ddb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W442TR7LXXP6DTPEB4TCA2EHAH/bundle.json","state_url":"https://pith.science/pith/W442TR7LXXP6DTPEB4TCA2EHAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W442TR7LXXP6DTPEB4TCA2EHAH/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":"2026-05-27T22:57:22Z","links":{"resolver":"https://pith.science/pith/W442TR7LXXP6DTPEB4TCA2EHAH","bundle":"https://pith.science/pith/W442TR7LXXP6DTPEB4TCA2EHAH/bundle.json","state":"https://pith.science/pith/W442TR7LXXP6DTPEB4TCA2EHAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W442TR7LXXP6DTPEB4TCA2EHAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W442TR7LXXP6DTPEB4TCA2EHAH","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":"672aa67f5e591ffe276bf4f3a7b46247a1bc95bf6724ad3cac09241b8067b863","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T18:50:55Z","title_canon_sha256":"bda462533ed3bf48db238e785ccd061235817184d46478c5c0e69e07629d0083"},"schema_version":"1.0","source":{"id":"1204.1305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1305","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1305v2","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1305","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"W442TR7LXXP6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W442TR7LXXP6DTPE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W442TR7L","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f1865ccd5bbae58e4d44c4a3d31857bf10196b5d20a999d0bcfe5e4cab123ddb","target":"graph","created_at":"2026-05-18T02:20:48Z","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 microlocal limits of plane waves on noncompact Riemannian manifolds (M,g) which are either Euclidean or asymptotically hyperbolic with curvature -1 near infinity. The plane waves E(z,\\xi) are functions on M parametrized by the square root of energy z and the direction of the wave, \\xi, interpreted as a point at infinity. If the trapped set K for the geodesic flow has Liouville measure zero, we show that, as z\\to +\\infty, E(z,\\xi) microlocally converges to a measure \\mu_\\xi, in average on energy intervals of fixed size, [z,z+1], and in \\xi. We express the rate of convergence to the lim","authors_text":"Colin Guillarmou, Semyon Dyatlov","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T18:50:55Z","title":"Microlocal limits of plane waves and Eisenstein functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1305","kind":"arxiv","version":2},"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:eb4f161fe365dd419c8bc77e94a81f8c9ab7dd24a8eba662ada3049ddedbae5b","target":"record","created_at":"2026-05-18T02:20:48Z","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":"672aa67f5e591ffe276bf4f3a7b46247a1bc95bf6724ad3cac09241b8067b863","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-05T18:50:55Z","title_canon_sha256":"bda462533ed3bf48db238e785ccd061235817184d46478c5c0e69e07629d0083"},"schema_version":"1.0","source":{"id":"1204.1305","kind":"arxiv","version":2}},"canonical_sha256":"b739a9c7ebbddfe1cde40f2620688701f4b06913b208ad1c67190c171ccba2e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b739a9c7ebbddfe1cde40f2620688701f4b06913b208ad1c67190c171ccba2e0","first_computed_at":"2026-05-18T02:20:48.028786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:48.028786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GiEKdY55G1050MA7r1N0UwNVqy778oNkYb7uaBDDB6RGSbtXSoVSmKmhiHeVKogrEfYgBYgIzrkVtv87UP8JAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:48.029533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb4f161fe365dd419c8bc77e94a81f8c9ab7dd24a8eba662ada3049ddedbae5b","sha256:f1865ccd5bbae58e4d44c4a3d31857bf10196b5d20a999d0bcfe5e4cab123ddb"],"state_sha256":"b1fdf64655216f59f0316a920f58b7520eb7e958eec433a174945a23e7a8d210"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEGLaiguqEHtzC9uHaIPG+MiYAzlMHBZF8s0VDAo0g2t1/DMXV+EIv527j38CY2HH0fRJ6uy9d/i+Jfi+bAqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:57:22.090771Z","bundle_sha256":"7b2f988e71a834382ae56ec15e8d7c04f511969fa24dfb340cd839b79d709da1"}}