{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NJK2CLJOQXXGAJSTATJQUM45CY","short_pith_number":"pith:NJK2CLJO","canonical_record":{"source":{"id":"1408.3383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-14T18:54:56Z","cross_cats_sorted":[],"title_canon_sha256":"191806b24c6e3a8ade320e8bad05a50467fa813022232b1df8a3eb702dc6b04c","abstract_canon_sha256":"151706578e0202ef5754317393d77bb6ae396710e5669a62ce73527323150c25"},"schema_version":"1.0"},"canonical_sha256":"6a55a12d2e85ee60265304d30a339d162558f83cdf4e5030896c29897a1d7771","source":{"kind":"arxiv","id":"1408.3383","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3383","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3383v3","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3383","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"NJK2CLJOQXXG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NJK2CLJOQXXGAJST","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NJK2CLJO","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NJK2CLJOQXXGAJSTATJQUM45CY","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-14T18:54:56Z","cross_cats_sorted":[],"title_canon_sha256":"191806b24c6e3a8ade320e8bad05a50467fa813022232b1df8a3eb702dc6b04c","abstract_canon_sha256":"151706578e0202ef5754317393d77bb6ae396710e5669a62ce73527323150c25"},"schema_version":"1.0"},"canonical_sha256":"6a55a12d2e85ee60265304d30a339d162558f83cdf4e5030896c29897a1d7771","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:41.798226Z","signature_b64":"fH8SiFKDNGsmXe3fsxc/DAH2W4vQUG6U9/u+1rVLa0zoa66svfnLeOABt7RIxurWz/Iu+2JP+UOmfCDkwUCBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a55a12d2e85ee60265304d30a339d162558f83cdf4e5030896c29897a1d7771","last_reissued_at":"2026-05-18T01:32:41.797686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:41.797686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3383","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":"2026-05-18T01:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"al0k5aJ1Kha5ByD1rt9RfCtX/I2RyKxZ5ZnmD5d/UB6LaeW9gzZAe2xRVHNwvHJfzazslMQ8FO2XIcsd7PKCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:29:43.200218Z"},"content_sha256":"a07c2fd72b3ede55a9e24c267efcef390cfcaa4241d67f6678a967ed8fceaebe","schema_version":"1.0","event_id":"sha256:a07c2fd72b3ede55a9e24c267efcef390cfcaa4241d67f6678a967ed8fceaebe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NJK2CLJOQXXGAJSTATJQUM45CY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tameness, Uniqueness and amalgamation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Adi Jarden","submitted_at":"2014-08-14T18:54:56Z","abstract_excerpt":"We combine two approaches to the study of classification theory of AECs: 1. that of Shelah: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and 2. that of Grossberg and VanDieren: (studying non-splitting) assuming the amalgamation property and tameness. In [JrSh875], we derive a good non-forking $\\lambda^+$-frame from a semi-good non-forking $\\lambda$-frame. But the classes $K_{\\lambda^+}$ and $\\preceq \\restriction K_{\\lambda^+}$ are replaced: $K_{\\lambda^+}$ is restricted to the saturated models and the partial order $\\pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3383","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":"2026-05-18T01:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKSqdOovIWEfVq19GyeyTUuNHavmX+FjaZerFhejDkN7DC6pEzMAOj37kaygblwBcuviqymTosWkZ+ausGjnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:29:43.200582Z"},"content_sha256":"e4c5e2625d2593286bb9d516a436e916e03d1ed37c71b4ac44ef09372820fbbe","schema_version":"1.0","event_id":"sha256:e4c5e2625d2593286bb9d516a436e916e03d1ed37c71b4ac44ef09372820fbbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJK2CLJOQXXGAJSTATJQUM45CY/bundle.json","state_url":"https://pith.science/pith/NJK2CLJOQXXGAJSTATJQUM45CY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJK2CLJOQXXGAJSTATJQUM45CY/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":"2026-06-01T09:29:43Z","links":{"resolver":"https://pith.science/pith/NJK2CLJOQXXGAJSTATJQUM45CY","bundle":"https://pith.science/pith/NJK2CLJOQXXGAJSTATJQUM45CY/bundle.json","state":"https://pith.science/pith/NJK2CLJOQXXGAJSTATJQUM45CY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJK2CLJOQXXGAJSTATJQUM45CY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NJK2CLJOQXXGAJSTATJQUM45CY","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":"151706578e0202ef5754317393d77bb6ae396710e5669a62ce73527323150c25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-14T18:54:56Z","title_canon_sha256":"191806b24c6e3a8ade320e8bad05a50467fa813022232b1df8a3eb702dc6b04c"},"schema_version":"1.0","source":{"id":"1408.3383","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3383","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3383v3","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3383","created_at":"2026-05-18T01:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"NJK2CLJOQXXG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NJK2CLJOQXXGAJST","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NJK2CLJO","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:e4c5e2625d2593286bb9d516a436e916e03d1ed37c71b4ac44ef09372820fbbe","target":"graph","created_at":"2026-05-18T01:32:41Z","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 combine two approaches to the study of classification theory of AECs: 1. that of Shelah: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and 2. that of Grossberg and VanDieren: (studying non-splitting) assuming the amalgamation property and tameness. In [JrSh875], we derive a good non-forking $\\lambda^+$-frame from a semi-good non-forking $\\lambda$-frame. But the classes $K_{\\lambda^+}$ and $\\preceq \\restriction K_{\\lambda^+}$ are replaced: $K_{\\lambda^+}$ is restricted to the saturated models and the partial order $\\pr","authors_text":"Adi Jarden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-14T18:54:56Z","title":"Tameness, Uniqueness and amalgamation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3383","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:a07c2fd72b3ede55a9e24c267efcef390cfcaa4241d67f6678a967ed8fceaebe","target":"record","created_at":"2026-05-18T01:32:41Z","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":"151706578e0202ef5754317393d77bb6ae396710e5669a62ce73527323150c25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-14T18:54:56Z","title_canon_sha256":"191806b24c6e3a8ade320e8bad05a50467fa813022232b1df8a3eb702dc6b04c"},"schema_version":"1.0","source":{"id":"1408.3383","kind":"arxiv","version":3}},"canonical_sha256":"6a55a12d2e85ee60265304d30a339d162558f83cdf4e5030896c29897a1d7771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a55a12d2e85ee60265304d30a339d162558f83cdf4e5030896c29897a1d7771","first_computed_at":"2026-05-18T01:32:41.797686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:41.797686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fH8SiFKDNGsmXe3fsxc/DAH2W4vQUG6U9/u+1rVLa0zoa66svfnLeOABt7RIxurWz/Iu+2JP+UOmfCDkwUCBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:41.798226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3383","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a07c2fd72b3ede55a9e24c267efcef390cfcaa4241d67f6678a967ed8fceaebe","sha256:e4c5e2625d2593286bb9d516a436e916e03d1ed37c71b4ac44ef09372820fbbe"],"state_sha256":"67494470e4d881f9c126356f88b19a9b229a25a0619d3a2a2d141849dafe33e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuIWBXzjArLkElK6bmLdUaJv02ghoBGbQoOL1Wkr+QjXZaeCIfHh31REi8QRA5L1xSZR4XDFRjrzkkSW0lEKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:29:43.202629Z","bundle_sha256":"b4d1e6878408b96765474130b2a77a362906c481247dd744bea072e4fcf648b5"}}