{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:THGMJ66BBDN74HMEP4H66XLOAO","short_pith_number":"pith:THGMJ66B","canonical_record":{"source":{"id":"1611.02270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2016-11-02T01:50:07Z","cross_cats_sorted":[],"title_canon_sha256":"c43b8b50ffc1a092feb1048fc6cd5b1a2b909dbe8051b6ede09ad3a833266121","abstract_canon_sha256":"ea0909b629a2f99cf57d8b79da28bc619cc91b3c840da789f32850cde2d37253"},"schema_version":"1.0"},"canonical_sha256":"99ccc4fbc108dbfe1d847f0fef5d6e0382927aee0baff9e4312f1b25a2fc5733","source":{"kind":"arxiv","id":"1611.02270","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02270","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02270v2","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02270","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"THGMJ66BBDN7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"THGMJ66BBDN74HME","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"THGMJ66B","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:THGMJ66BBDN74HMEP4H66XLOAO","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2016-11-02T01:50:07Z","cross_cats_sorted":[],"title_canon_sha256":"c43b8b50ffc1a092feb1048fc6cd5b1a2b909dbe8051b6ede09ad3a833266121","abstract_canon_sha256":"ea0909b629a2f99cf57d8b79da28bc619cc91b3c840da789f32850cde2d37253"},"schema_version":"1.0"},"canonical_sha256":"99ccc4fbc108dbfe1d847f0fef5d6e0382927aee0baff9e4312f1b25a2fc5733","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:51.025229Z","signature_b64":"04p+rSK2QpVHoSSeFnl+a6uF7H8qB+98c2h3k5xcUZwZ6EzCI4aXm0BIuRRR3wg2i/zIXQfU8qlgD9ReJzpgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ccc4fbc108dbfe1d847f0fef5d6e0382927aee0baff9e4312f1b25a2fc5733","last_reissued_at":"2026-05-18T00:07:51.024332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:51.024332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02270","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":"2026-05-18T00:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzWqJ4+jFAq4heGSX77hS0sU13vbxiY3BfFE32Wo+DKXhoaRI+LzSF7gp8R3Jr0lLJe5tIR/rpzkL9gnkrKvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:35:56.280263Z"},"content_sha256":"7454618537f52f7ef99a403d01116b561b3103357c03242a6927130957429cd0","schema_version":"1.0","event_id":"sha256:7454618537f52f7ef99a403d01116b561b3103357c03242a6927130957429cd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:THGMJ66BBDN74HMEP4H66XLOAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional Forms for Tractable Economic Models and the Cost Structure of International Trade","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.EC","authors_text":"E. Glen Weyl, Michal Fabinger","submitted_at":"2016-11-02T01:50:07Z","abstract_excerpt":"We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational subroutines. We use the latter approach to build a tractable heterogeneous firm model of international trade accommodating economies of scale in export and diseconomies of scale in production, providing a natural, unified solution to several puzzles concerning trade costs. We briefly highlight applications in a range of other fields. Our method of generating analyti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02270","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":"2026-05-18T00:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DxN6tuKSoJKCQQsTFxfHDCxgS+D0poL7Lo7+5km/gGIP0zEnHb8WC8KPs9oBiz3EgvY+WGdDuB6DPTFrfoyQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:35:56.280837Z"},"content_sha256":"29f8aa95cf23998aa8f456cc1e31ed915139ad10d942bcab6b14273f49fcad2c","schema_version":"1.0","event_id":"sha256:29f8aa95cf23998aa8f456cc1e31ed915139ad10d942bcab6b14273f49fcad2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THGMJ66BBDN74HMEP4H66XLOAO/bundle.json","state_url":"https://pith.science/pith/THGMJ66BBDN74HMEP4H66XLOAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THGMJ66BBDN74HMEP4H66XLOAO/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":"2026-05-27T16:35:56Z","links":{"resolver":"https://pith.science/pith/THGMJ66BBDN74HMEP4H66XLOAO","bundle":"https://pith.science/pith/THGMJ66BBDN74HMEP4H66XLOAO/bundle.json","state":"https://pith.science/pith/THGMJ66BBDN74HMEP4H66XLOAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THGMJ66BBDN74HMEP4H66XLOAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:THGMJ66BBDN74HMEP4H66XLOAO","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":"ea0909b629a2f99cf57d8b79da28bc619cc91b3c840da789f32850cde2d37253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2016-11-02T01:50:07Z","title_canon_sha256":"c43b8b50ffc1a092feb1048fc6cd5b1a2b909dbe8051b6ede09ad3a833266121"},"schema_version":"1.0","source":{"id":"1611.02270","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02270","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02270v2","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02270","created_at":"2026-05-18T00:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"THGMJ66BBDN7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"THGMJ66BBDN74HME","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"THGMJ66B","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:29f8aa95cf23998aa8f456cc1e31ed915139ad10d942bcab6b14273f49fcad2c","target":"graph","created_at":"2026-05-18T00:07:51Z","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 present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational subroutines. We use the latter approach to build a tractable heterogeneous firm model of international trade accommodating economies of scale in export and diseconomies of scale in production, providing a natural, unified solution to several puzzles concerning trade costs. We briefly highlight applications in a range of other fields. Our method of generating analyti","authors_text":"E. Glen Weyl, Michal Fabinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2016-11-02T01:50:07Z","title":"Functional Forms for Tractable Economic Models and the Cost Structure of International Trade"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02270","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":"sha256:7454618537f52f7ef99a403d01116b561b3103357c03242a6927130957429cd0","target":"record","created_at":"2026-05-18T00:07:51Z","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":"ea0909b629a2f99cf57d8b79da28bc619cc91b3c840da789f32850cde2d37253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2016-11-02T01:50:07Z","title_canon_sha256":"c43b8b50ffc1a092feb1048fc6cd5b1a2b909dbe8051b6ede09ad3a833266121"},"schema_version":"1.0","source":{"id":"1611.02270","kind":"arxiv","version":2}},"canonical_sha256":"99ccc4fbc108dbfe1d847f0fef5d6e0382927aee0baff9e4312f1b25a2fc5733","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ccc4fbc108dbfe1d847f0fef5d6e0382927aee0baff9e4312f1b25a2fc5733","first_computed_at":"2026-05-18T00:07:51.024332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:51.024332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04p+rSK2QpVHoSSeFnl+a6uF7H8qB+98c2h3k5xcUZwZ6EzCI4aXm0BIuRRR3wg2i/zIXQfU8qlgD9ReJzpgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:51.025229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02270","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7454618537f52f7ef99a403d01116b561b3103357c03242a6927130957429cd0","sha256:29f8aa95cf23998aa8f456cc1e31ed915139ad10d942bcab6b14273f49fcad2c"],"state_sha256":"b922d91c91033c421ff4df2ed2cf5fce2e0d4fc87e948f85cc93debae4843442"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gelTTrpRcvC9bluX6TgKNUdxrt38UT2QUVAAb2y8VsB4jy5kFlpYsTv5mkOddZckDYOoyfwFa/MLP+ZxoX82Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:35:56.284286Z","bundle_sha256":"1df073efeed13b33e99165014a5944ea227f39a3a98897f4a0c80d09ad5e9fc4"}}