{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CO6427FGYSSK3QWLFEABTVPL7R","short_pith_number":"pith:CO6427FG","canonical_record":{"source":{"id":"2507.12025","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-16T08:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"cb96bb2ec4a367086aa35ad853c31cc395e5e2f8f597524d6271bc226ca07308","abstract_canon_sha256":"aac7c02e1d760845700b5c51a3d26363e6eb55610c1a4b676c70845eda10c04d"},"schema_version":"1.0"},"canonical_sha256":"13bdcd7ca6c4a4adc2cb290019d5ebfc633a87c01a9d5b36ee638debfa4788a7","source":{"kind":"arxiv","id":"2507.12025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12025","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12025v1","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12025","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"CO6427FGYSSK","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_16","alias_value":"CO6427FGYSSK3QWL","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_8","alias_value":"CO6427FG","created_at":"2026-07-05T11:38:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CO6427FGYSSK3QWLFEABTVPL7R","target":"record","payload":{"canonical_record":{"source":{"id":"2507.12025","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-16T08:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"cb96bb2ec4a367086aa35ad853c31cc395e5e2f8f597524d6271bc226ca07308","abstract_canon_sha256":"aac7c02e1d760845700b5c51a3d26363e6eb55610c1a4b676c70845eda10c04d"},"schema_version":"1.0"},"canonical_sha256":"13bdcd7ca6c4a4adc2cb290019d5ebfc633a87c01a9d5b36ee638debfa4788a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:13.234556Z","signature_b64":"r+k4PdzZrGdeJzcBIaasE03+lXvaMGsaHBI27BkBvRnRgVXxLHxcxHuZeDO007pQLtJntEs/rZGMYlXiOR8yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13bdcd7ca6c4a4adc2cb290019d5ebfc633a87c01a9d5b36ee638debfa4788a7","last_reissued_at":"2026-07-05T11:38:13.233998Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:13.233998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.12025","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":"2026-07-05T11:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4mzaUQQtkBdt6zgsnvSFmbwp4lEHIgf1YZ36y18yoqyjpP7peRq3SSAfmCUUqoEHshLlQZjbGDrapFkQumzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T19:47:11.736713Z"},"content_sha256":"2fc13b9ffb814f0294f9a886904d072b65019d2aea62884507e24f05f8f5ea6f","schema_version":"1.0","event_id":"sha256:2fc13b9ffb814f0294f9a886904d072b65019d2aea62884507e24f05f8f5ea6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CO6427FGYSSK3QWLFEABTVPL7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying the complexity of models of arithmetic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Gonzalez, Dino Rossegger, Mateusz {\\L}e{\\l}yk, Patryk Szlufik","submitted_at":"2025-07-16T08:38:18Z","abstract_excerpt":"We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic from these colored orderings. We also provide tight connections of certain Scott complexities with notions from the classical theory of models of Peano arithmetic, such as prime, finitely generated, and recursively saturated. This effort provides a powerful set of tools to understand the models of Peano arithmetic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12025","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/2507.12025/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":"2026-07-05T11:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WI4huJ2pXv9f992DPgKjoLP8CwPGyHOHTjtXEkkUzPVFYOCLldtTjjDbOxJQhPEQofnXKQfafBshwoeHenvoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T19:47:11.737228Z"},"content_sha256":"a4f044cd62f55d8b9aee662c5a5fe1c62ea41c2ac904f558770090c13ed7fdd6","schema_version":"1.0","event_id":"sha256:a4f044cd62f55d8b9aee662c5a5fe1c62ea41c2ac904f558770090c13ed7fdd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO6427FGYSSK3QWLFEABTVPL7R/bundle.json","state_url":"https://pith.science/pith/CO6427FGYSSK3QWLFEABTVPL7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO6427FGYSSK3QWLFEABTVPL7R/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":"2026-08-05T19:47:11Z","links":{"resolver":"https://pith.science/pith/CO6427FGYSSK3QWLFEABTVPL7R","bundle":"https://pith.science/pith/CO6427FGYSSK3QWLFEABTVPL7R/bundle.json","state":"https://pith.science/pith/CO6427FGYSSK3QWLFEABTVPL7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO6427FGYSSK3QWLFEABTVPL7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CO6427FGYSSK3QWLFEABTVPL7R","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":"aac7c02e1d760845700b5c51a3d26363e6eb55610c1a4b676c70845eda10c04d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-16T08:38:18Z","title_canon_sha256":"cb96bb2ec4a367086aa35ad853c31cc395e5e2f8f597524d6271bc226ca07308"},"schema_version":"1.0","source":{"id":"2507.12025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12025","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12025v1","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12025","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"CO6427FGYSSK","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_16","alias_value":"CO6427FGYSSK3QWL","created_at":"2026-07-05T11:38:13Z"},{"alias_kind":"pith_short_8","alias_value":"CO6427FG","created_at":"2026-07-05T11:38:13Z"}],"graph_snapshots":[{"event_id":"sha256:a4f044cd62f55d8b9aee662c5a5fe1c62ea41c2ac904f558770090c13ed7fdd6","target":"graph","created_at":"2026-07-05T11:38:13Z","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/2507.12025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We classify the possible Scott complexities for models of Peano arithmetic. We construct models of particular complexities by first giving a complete Scott analysis of colored linear orderings and constructing models of Peano arithmetic from these colored orderings. We also provide tight connections of certain Scott complexities with notions from the classical theory of models of Peano arithmetic, such as prime, finitely generated, and recursively saturated. This effort provides a powerful set of tools to understand the models of Peano arithmetic.","authors_text":"David Gonzalez, Dino Rossegger, Mateusz {\\L}e{\\l}yk, Patryk Szlufik","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-16T08:38:18Z","title":"Classifying the complexity of models of arithmetic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12025","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":"sha256:2fc13b9ffb814f0294f9a886904d072b65019d2aea62884507e24f05f8f5ea6f","target":"record","created_at":"2026-07-05T11:38:13Z","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":"aac7c02e1d760845700b5c51a3d26363e6eb55610c1a4b676c70845eda10c04d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-16T08:38:18Z","title_canon_sha256":"cb96bb2ec4a367086aa35ad853c31cc395e5e2f8f597524d6271bc226ca07308"},"schema_version":"1.0","source":{"id":"2507.12025","kind":"arxiv","version":1}},"canonical_sha256":"13bdcd7ca6c4a4adc2cb290019d5ebfc633a87c01a9d5b36ee638debfa4788a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13bdcd7ca6c4a4adc2cb290019d5ebfc633a87c01a9d5b36ee638debfa4788a7","first_computed_at":"2026-07-05T11:38:13.233998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:13.233998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r+k4PdzZrGdeJzcBIaasE03+lXvaMGsaHBI27BkBvRnRgVXxLHxcxHuZeDO007pQLtJntEs/rZGMYlXiOR8yDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:13.234556Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fc13b9ffb814f0294f9a886904d072b65019d2aea62884507e24f05f8f5ea6f","sha256:a4f044cd62f55d8b9aee662c5a5fe1c62ea41c2ac904f558770090c13ed7fdd6"],"state_sha256":"a43729df092640ba361bc12e1524f7c1346e9a9420b073f43f8163241e39dd51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yk1tEplMSCprhkKUiNVnAL4i3iyGovM696zNBzwYAqEUQN4IwlUStxIfVHIQVutpi8FBHEKGiPrlfv/8C96oAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T19:47:11.742495Z","bundle_sha256":"045f0e5421269c97db55d7c1b48cdc87d0bf7da3eb3f11c745a1b54a9dd02a9b"}}