{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GPV56VVFURK4YVS4YQNHYVIT6X","short_pith_number":"pith:GPV56VVF","canonical_record":{"source":{"id":"1411.7654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-27T17:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"4febbb84671e8580d08ddecf23c1536055e5443276ee3a1bdc86dd5a95c33c05","abstract_canon_sha256":"68a0f292a7d7177c51f8ec91878f972a182797e124baeec80854ddadc3eff2ad"},"schema_version":"1.0"},"canonical_sha256":"33ebdf56a5a455cc565cc41a7c5513f5d51507d16691a6316bd1ad0156f24b46","source":{"kind":"arxiv","id":"1411.7654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7654","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7654v2","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7654","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"GPV56VVFURK4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GPV56VVFURK4YVS4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GPV56VVF","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GPV56VVFURK4YVS4YQNHYVIT6X","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-27T17:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"4febbb84671e8580d08ddecf23c1536055e5443276ee3a1bdc86dd5a95c33c05","abstract_canon_sha256":"68a0f292a7d7177c51f8ec91878f972a182797e124baeec80854ddadc3eff2ad"},"schema_version":"1.0"},"canonical_sha256":"33ebdf56a5a455cc565cc41a7c5513f5d51507d16691a6316bd1ad0156f24b46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:50.006656Z","signature_b64":"I0iHYBQ9BCi/hn7/9kI5Q06JfeOu2ojPkRVcOSC840VP8POE2rh6XXwkwZ9J7tbvl+NeUXxkXcN1LxuthRvACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33ebdf56a5a455cc565cc41a7c5513f5d51507d16691a6316bd1ad0156f24b46","last_reissued_at":"2026-05-18T01:02:50.006126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:50.006126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7654","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":"2026-05-18T01:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IW685xaEPuGo/lUxdbuebYCN+YRJa4bPpF+UF/8JGVI/FuYsbO5xNzNL9LR9xxQKC53sjMxvHRXgCn8O1tZCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:56.520219Z"},"content_sha256":"a1683e5976c8350d8f024171ee8890ad3bc0ef08d60c929bbc83b0968c741389","schema_version":"1.0","event_id":"sha256:a1683e5976c8350d8f024171ee8890ad3bc0ef08d60c929bbc83b0968c741389"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GPV56VVFURK4YVS4YQNHYVIT6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudo real closed field, pseudo p-adically closed fields and NTP2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Samaria Montenegro","submitted_at":"2014-11-27T17:21:07Z","abstract_excerpt":"The main result of this paper is a positive answer to the Conjecture 5.1 by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP_2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then Th(M) is NTP_2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7654","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":"2026-05-18T01:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDK0y4k9eAJxUan9B6bE6ZBcEqbyYNlAIPCjgPza4n4/u8zpIQF08HnIN7Q90a5YF+Ehxxtyksl+ovYUe0T3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:54:56.520869Z"},"content_sha256":"00b1db1dddfc6164b4fe67abd8572ca9421caa4c0352aecfc272ebb843f0f879","schema_version":"1.0","event_id":"sha256:00b1db1dddfc6164b4fe67abd8572ca9421caa4c0352aecfc272ebb843f0f879"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPV56VVFURK4YVS4YQNHYVIT6X/bundle.json","state_url":"https://pith.science/pith/GPV56VVFURK4YVS4YQNHYVIT6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPV56VVFURK4YVS4YQNHYVIT6X/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":"2026-05-27T11:54:56Z","links":{"resolver":"https://pith.science/pith/GPV56VVFURK4YVS4YQNHYVIT6X","bundle":"https://pith.science/pith/GPV56VVFURK4YVS4YQNHYVIT6X/bundle.json","state":"https://pith.science/pith/GPV56VVFURK4YVS4YQNHYVIT6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPV56VVFURK4YVS4YQNHYVIT6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GPV56VVFURK4YVS4YQNHYVIT6X","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":"68a0f292a7d7177c51f8ec91878f972a182797e124baeec80854ddadc3eff2ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-27T17:21:07Z","title_canon_sha256":"4febbb84671e8580d08ddecf23c1536055e5443276ee3a1bdc86dd5a95c33c05"},"schema_version":"1.0","source":{"id":"1411.7654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7654","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7654v2","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7654","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"GPV56VVFURK4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GPV56VVFURK4YVS4","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GPV56VVF","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:00b1db1dddfc6164b4fe67abd8572ca9421caa4c0352aecfc272ebb843f0f879","target":"graph","created_at":"2026-05-18T01:02:50Z","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":"The main result of this paper is a positive answer to the Conjecture 5.1 by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP_2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then Th(M) is NTP_2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking.","authors_text":"Samaria Montenegro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-27T17:21:07Z","title":"Pseudo real closed field, pseudo p-adically closed fields and NTP2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7654","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:a1683e5976c8350d8f024171ee8890ad3bc0ef08d60c929bbc83b0968c741389","target":"record","created_at":"2026-05-18T01:02:50Z","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":"68a0f292a7d7177c51f8ec91878f972a182797e124baeec80854ddadc3eff2ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-27T17:21:07Z","title_canon_sha256":"4febbb84671e8580d08ddecf23c1536055e5443276ee3a1bdc86dd5a95c33c05"},"schema_version":"1.0","source":{"id":"1411.7654","kind":"arxiv","version":2}},"canonical_sha256":"33ebdf56a5a455cc565cc41a7c5513f5d51507d16691a6316bd1ad0156f24b46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33ebdf56a5a455cc565cc41a7c5513f5d51507d16691a6316bd1ad0156f24b46","first_computed_at":"2026-05-18T01:02:50.006126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:50.006126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I0iHYBQ9BCi/hn7/9kI5Q06JfeOu2ojPkRVcOSC840VP8POE2rh6XXwkwZ9J7tbvl+NeUXxkXcN1LxuthRvACw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:50.006656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1683e5976c8350d8f024171ee8890ad3bc0ef08d60c929bbc83b0968c741389","sha256:00b1db1dddfc6164b4fe67abd8572ca9421caa4c0352aecfc272ebb843f0f879"],"state_sha256":"b70a7a5aa163b5e8f466456ddcb01fa34cb1eaaeb8736a7c41de83b467625db3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOrZJCcs9EeWOldWqdofaQlEbS/xwnMmw8+gaJG2cmNM7lb1Sg5w8r/EOjE4c07j6SWVBv03ndn7YAq/mGpWCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:54:56.524160Z","bundle_sha256":"dc34aa243198c452c6210f83c24754aa4cde42869155ee95c464dbe3c22d86b7"}}