{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ENKH7YWAL5UPLCTG2S4RKMRKNB","short_pith_number":"pith:ENKH7YWA","canonical_record":{"source":{"id":"2209.03944","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-08T17:36:39Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4fea84f02bec83b00f94ecff64bc8dd75ca4a27e0a1876f0e002171fa525f0b0","abstract_canon_sha256":"c02e3413cdbe6821473f4e893a8aa940ab54788ae942a928e6125153773e490f"},"schema_version":"1.0"},"canonical_sha256":"23547fe2c05f68f58a66d4b915322a6854c5a298ec98b48b5102586360ac6657","source":{"kind":"arxiv","id":"2209.03944","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.03944","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"2209.03944v5","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.03944","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"ENKH7YWAL5UP","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_16","alias_value":"ENKH7YWAL5UPLCTG","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_8","alias_value":"ENKH7YWA","created_at":"2026-06-29T01:13:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ENKH7YWAL5UPLCTG2S4RKMRKNB","target":"record","payload":{"canonical_record":{"source":{"id":"2209.03944","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-08T17:36:39Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"4fea84f02bec83b00f94ecff64bc8dd75ca4a27e0a1876f0e002171fa525f0b0","abstract_canon_sha256":"c02e3413cdbe6821473f4e893a8aa940ab54788ae942a928e6125153773e490f"},"schema_version":"1.0"},"canonical_sha256":"23547fe2c05f68f58a66d4b915322a6854c5a298ec98b48b5102586360ac6657","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:13:59.810150Z","signature_b64":"yxIZdvtIaFiBJRPzxDlzNCVRXt5tKt+ZBALWFd6+tY3c+efTQ7qd0HBJEmKlOhwtYujCCAZOAEHFl/ir16d6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23547fe2c05f68f58a66d4b915322a6854c5a298ec98b48b5102586360ac6657","last_reissued_at":"2026-06-29T01:13:59.809652Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:13:59.809652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.03944","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-29T01:13:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pN9jPlLzlz6GttQInwIr+kEIeXVzoCBzT96CR+JM1WGcc5ZFtG2paFaei8NzZ8/6Z+c/G2Boc6TduYa0kGX/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T03:29:36.831295Z"},"content_sha256":"b21384929d85e40298078f982aee889261288d4515c0c6b7edf8d1c4f8f7f96a","schema_version":"1.0","event_id":"sha256:b21384929d85e40298078f982aee889261288d4515c0c6b7edf8d1c4f8f7f96a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ENKH7YWAL5UPLCTG2S4RKMRKNB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Amalgamation Property for automorphisms of ordered abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Jan Dobrowolski, Rosario Mennuni","submitted_at":"2022-09-08T17:36:39Z","abstract_excerpt":"We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is NIP in the sense of positive logic, and initiate a development of the latter framework.\n  As byproducts of the proof, we obtain a generalised version of the Hahn Embedding Theorem which allows to lift each automorphism of an ordered abelian group to one of an ordered real vector space, and we show that, on existentially closed structures, linear combinations of iterates of the automorphism have the Intermediate Value Property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.03944","kind":"arxiv","version":5},"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/2209.03944/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":"2026-06-29T01:13:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mD7lD8bUBOo1od9GTUZwNZZiE1t2sG1Joq6/beMbA4K5cSHygr2G6tHMx6dR5H7vvyeYunJJYOxLafZQ7LWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T03:29:36.831677Z"},"content_sha256":"e677db5cfae3adc7fedeb4c7d27681b306f26fdf0206ce5a123cf4fca5533cbf","schema_version":"1.0","event_id":"sha256:e677db5cfae3adc7fedeb4c7d27681b306f26fdf0206ce5a123cf4fca5533cbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/bundle.json","state_url":"https://pith.science/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/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":"2026-07-03T03:29:36Z","links":{"resolver":"https://pith.science/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB","bundle":"https://pith.science/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/bundle.json","state":"https://pith.science/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENKH7YWAL5UPLCTG2S4RKMRKNB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ENKH7YWAL5UPLCTG2S4RKMRKNB","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":"c02e3413cdbe6821473f4e893a8aa940ab54788ae942a928e6125153773e490f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-08T17:36:39Z","title_canon_sha256":"4fea84f02bec83b00f94ecff64bc8dd75ca4a27e0a1876f0e002171fa525f0b0"},"schema_version":"1.0","source":{"id":"2209.03944","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.03944","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"arxiv_version","alias_value":"2209.03944v5","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.03944","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_12","alias_value":"ENKH7YWAL5UP","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_16","alias_value":"ENKH7YWAL5UPLCTG","created_at":"2026-06-29T01:13:59Z"},{"alias_kind":"pith_short_8","alias_value":"ENKH7YWA","created_at":"2026-06-29T01:13:59Z"}],"graph_snapshots":[{"event_id":"sha256:e677db5cfae3adc7fedeb4c7d27681b306f26fdf0206ce5a123cf4fca5533cbf","target":"graph","created_at":"2026-06-29T01:13:59Z","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/2209.03944/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is NIP in the sense of positive logic, and initiate a development of the latter framework.\n  As byproducts of the proof, we obtain a generalised version of the Hahn Embedding Theorem which allows to lift each automorphism of an ordered abelian group to one of an ordered real vector space, and we show that, on existentially closed structures, linear combinations of iterates of the automorphism have the Intermediate Value Property.","authors_text":"Jan Dobrowolski, Rosario Mennuni","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-08T17:36:39Z","title":"The Amalgamation Property for automorphisms of ordered abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.03944","kind":"arxiv","version":5},"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:b21384929d85e40298078f982aee889261288d4515c0c6b7edf8d1c4f8f7f96a","target":"record","created_at":"2026-06-29T01:13:59Z","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":"c02e3413cdbe6821473f4e893a8aa940ab54788ae942a928e6125153773e490f","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2022-09-08T17:36:39Z","title_canon_sha256":"4fea84f02bec83b00f94ecff64bc8dd75ca4a27e0a1876f0e002171fa525f0b0"},"schema_version":"1.0","source":{"id":"2209.03944","kind":"arxiv","version":5}},"canonical_sha256":"23547fe2c05f68f58a66d4b915322a6854c5a298ec98b48b5102586360ac6657","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23547fe2c05f68f58a66d4b915322a6854c5a298ec98b48b5102586360ac6657","first_computed_at":"2026-06-29T01:13:59.809652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:13:59.809652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxIZdvtIaFiBJRPzxDlzNCVRXt5tKt+ZBALWFd6+tY3c+efTQ7qd0HBJEmKlOhwtYujCCAZOAEHFl/ir16d6AQ==","signature_status":"signed_v1","signed_at":"2026-06-29T01:13:59.810150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.03944","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b21384929d85e40298078f982aee889261288d4515c0c6b7edf8d1c4f8f7f96a","sha256:e677db5cfae3adc7fedeb4c7d27681b306f26fdf0206ce5a123cf4fca5533cbf"],"state_sha256":"fb5289e4e5b0aabea21d310e22bd3e954da77dd8ac6de205ea8521ea40a8a4b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYOdgKedlfYwJV1XXiYDTXk31lQbRQH6ZPKlFJc10oByvfPEzsr5neyhKv+t2aICEppw7ktT7GGNHT1kCfptDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T03:29:36.833648Z","bundle_sha256":"3b6303c119f2e14322c3f50eeb3967105633d876fc642bfe56f0ed4e67af67b9"}}