{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3DQZR2O5D6A4J4VZEARVCPL42S","short_pith_number":"pith:3DQZR2O5","canonical_record":{"source":{"id":"2607.02095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2026-07-02T12:32:28Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"d8029c840984369c9cdf2f58cc0fe5ed1a163d7f29b1742374b9d33eac25a068","abstract_canon_sha256":"0afeafab1bb0d3429dbc3f42ea6a65b0428d21331f3a873f4fa15dcb8237a696"},"schema_version":"1.0"},"canonical_sha256":"d8e198e9dd1f81c4f2b92023513d7cd4ab3cab09843f7704c483be6b930b655d","source":{"kind":"arxiv","id":"2607.02095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02095","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02095v1","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02095","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"3DQZR2O5D6A4","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_16","alias_value":"3DQZR2O5D6A4J4VZ","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_8","alias_value":"3DQZR2O5","created_at":"2026-07-03T01:17:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3DQZR2O5D6A4J4VZEARVCPL42S","target":"record","payload":{"canonical_record":{"source":{"id":"2607.02095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2026-07-02T12:32:28Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"d8029c840984369c9cdf2f58cc0fe5ed1a163d7f29b1742374b9d33eac25a068","abstract_canon_sha256":"0afeafab1bb0d3429dbc3f42ea6a65b0428d21331f3a873f4fa15dcb8237a696"},"schema_version":"1.0"},"canonical_sha256":"d8e198e9dd1f81c4f2b92023513d7cd4ab3cab09843f7704c483be6b930b655d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:42.132010Z","signature_b64":"P33A3wQT/tFvfAfhybsyHE3y3CsDt989VhvZJDhiGOUYpb1GIT/AD2+J24KIs7kKIIEmfYBmGQgjQviBJ7fsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8e198e9dd1f81c4f2b92023513d7cd4ab3cab09843f7704c483be6b930b655d","last_reissued_at":"2026-07-03T01:17:42.131573Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:42.131573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.02095","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":"2026-07-03T01:17:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VeUK2ar/6vGLzoLSMqjgXjsI1TGeiX0+wvVuTG9EGrjv2TH9SY2bAFAQtQlq7oOBidtbmWBbrpBkI+h5O8TnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:59:16.021578Z"},"content_sha256":"ed16f1c26c1938db439ab8f82a8466e48ce7f64191438147cd45621c4dda0daa","schema_version":"1.0","event_id":"sha256:ed16f1c26c1938db439ab8f82a8466e48ce7f64191438147cd45621c4dda0daa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3DQZR2O5D6A4J4VZEARVCPL42S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Granular Instrumental Variables in Large Panels: Identification and Inference Across Strong, Nearly Weak, and Weak GIV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"econ.EM","authors_text":"Gokul Gopalan Ramachandran","submitted_at":"2026-07-02T12:32:28Z","abstract_excerpt":"I develop the asymptotic theory of instrument strength for Granular Instrumental Variables (GIV) in large panels with both $N$ and $T$ growing. The strength of the GIV depends on the presence of dominant units. I formalise what dominance means and characterise three regimes of instrument strength. When a few units dominate the aggregate, the instrument is strong. The GIV estimator is consistent and asymptotically normal at the standard $\\sqrt{T}$ rate. When large units stand out but do not dominate, the instrument weakens. But I show that the parameter of interest remains recoverable. The GIV "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02095","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/2607.02095/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":"2026-07-03T01:17:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c0Wrfrh1iJ3IJ1mygbcDs80vKuy9sSSdAdn0qAW0Hoc7OWL/XRe08UKfkUgToisyGE7t+kXge9W1GKvA2o1WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T08:59:16.021962Z"},"content_sha256":"fe8f73e4cd924b4dbea5dcb801dad683b6f6212e46b6c11a2df25ce944573a21","schema_version":"1.0","event_id":"sha256:fe8f73e4cd924b4dbea5dcb801dad683b6f6212e46b6c11a2df25ce944573a21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DQZR2O5D6A4J4VZEARVCPL42S/bundle.json","state_url":"https://pith.science/pith/3DQZR2O5D6A4J4VZEARVCPL42S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DQZR2O5D6A4J4VZEARVCPL42S/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":"2026-07-03T08:59:16Z","links":{"resolver":"https://pith.science/pith/3DQZR2O5D6A4J4VZEARVCPL42S","bundle":"https://pith.science/pith/3DQZR2O5D6A4J4VZEARVCPL42S/bundle.json","state":"https://pith.science/pith/3DQZR2O5D6A4J4VZEARVCPL42S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DQZR2O5D6A4J4VZEARVCPL42S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3DQZR2O5D6A4J4VZEARVCPL42S","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":"0afeafab1bb0d3429dbc3f42ea6a65b0428d21331f3a873f4fa15dcb8237a696","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2026-07-02T12:32:28Z","title_canon_sha256":"d8029c840984369c9cdf2f58cc0fe5ed1a163d7f29b1742374b9d33eac25a068"},"schema_version":"1.0","source":{"id":"2607.02095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02095","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02095v1","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02095","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"3DQZR2O5D6A4","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_16","alias_value":"3DQZR2O5D6A4J4VZ","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_8","alias_value":"3DQZR2O5","created_at":"2026-07-03T01:17:42Z"}],"graph_snapshots":[{"event_id":"sha256:fe8f73e4cd924b4dbea5dcb801dad683b6f6212e46b6c11a2df25ce944573a21","target":"graph","created_at":"2026-07-03T01:17:42Z","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/2607.02095/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I develop the asymptotic theory of instrument strength for Granular Instrumental Variables (GIV) in large panels with both $N$ and $T$ growing. The strength of the GIV depends on the presence of dominant units. I formalise what dominance means and characterise three regimes of instrument strength. When a few units dominate the aggregate, the instrument is strong. The GIV estimator is consistent and asymptotically normal at the standard $\\sqrt{T}$ rate. When large units stand out but do not dominate, the instrument weakens. But I show that the parameter of interest remains recoverable. The GIV ","authors_text":"Gokul Gopalan Ramachandran","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2026-07-02T12:32:28Z","title":"Granular Instrumental Variables in Large Panels: Identification and Inference Across Strong, Nearly Weak, and Weak GIV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02095","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:ed16f1c26c1938db439ab8f82a8466e48ce7f64191438147cd45621c4dda0daa","target":"record","created_at":"2026-07-03T01:17:42Z","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":"0afeafab1bb0d3429dbc3f42ea6a65b0428d21331f3a873f4fa15dcb8237a696","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2026-07-02T12:32:28Z","title_canon_sha256":"d8029c840984369c9cdf2f58cc0fe5ed1a163d7f29b1742374b9d33eac25a068"},"schema_version":"1.0","source":{"id":"2607.02095","kind":"arxiv","version":1}},"canonical_sha256":"d8e198e9dd1f81c4f2b92023513d7cd4ab3cab09843f7704c483be6b930b655d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8e198e9dd1f81c4f2b92023513d7cd4ab3cab09843f7704c483be6b930b655d","first_computed_at":"2026-07-03T01:17:42.131573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:42.131573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P33A3wQT/tFvfAfhybsyHE3y3CsDt989VhvZJDhiGOUYpb1GIT/AD2+J24KIs7kKIIEmfYBmGQgjQviBJ7fsAQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:42.132010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed16f1c26c1938db439ab8f82a8466e48ce7f64191438147cd45621c4dda0daa","sha256:fe8f73e4cd924b4dbea5dcb801dad683b6f6212e46b6c11a2df25ce944573a21"],"state_sha256":"d2ceeed5da5a25d002628e867a20526be57a3dbf82f8745ad67ff715e385a67b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHdFgC39HnXaRj5aecKtlTyiPpmYtRUcma24rOn6Q4eH+gWAvm8n1homjSY02zI2LbK9tGi+yXO7CPW1ZsKtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T08:59:16.026353Z","bundle_sha256":"77139e604adba14b251f5899e9525ec8fb4c43065f978217946657f5ab7a15ed"}}