{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ATJC6J6UTZOT6G5BGSQW3Y4S4I","short_pith_number":"pith:ATJC6J6U","canonical_record":{"source":{"id":"2606.02898","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T21:12:34Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b86fe640c6b356efb856d5b24feca10b892da9184ab0de01c18fd50d0fcf41a5","abstract_canon_sha256":"519d85313c19ea9c7b06ecab96d2ba220bffab9109f58ab195d045725dc45321"},"schema_version":"1.0"},"canonical_sha256":"04d22f27d49e5d3f1ba134a16de392e20bca2c70267aa610f493dc7f269c1238","source":{"kind":"arxiv","id":"2606.02898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02898","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02898v1","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02898","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"ATJC6J6UTZOT","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"ATJC6J6UTZOT6G5B","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"ATJC6J6U","created_at":"2026-06-03T01:05:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ATJC6J6UTZOT6G5BGSQW3Y4S4I","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02898","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T21:12:34Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b86fe640c6b356efb856d5b24feca10b892da9184ab0de01c18fd50d0fcf41a5","abstract_canon_sha256":"519d85313c19ea9c7b06ecab96d2ba220bffab9109f58ab195d045725dc45321"},"schema_version":"1.0"},"canonical_sha256":"04d22f27d49e5d3f1ba134a16de392e20bca2c70267aa610f493dc7f269c1238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:25.973223Z","signature_b64":"pBIUokd0RUwDkRtXW1uwLOQchUBnN9Hd0iYT2nS7DDynPt6HSDl1mvmVxbzd6diAfaCJRu2tc3ulFrrQ95aTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04d22f27d49e5d3f1ba134a16de392e20bca2c70267aa610f493dc7f269c1238","last_reissued_at":"2026-06-03T01:05:25.972810Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:25.972810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02898","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":"2026-06-03T01:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VxTEMN7D3Due0YMVLxKyyimODmczV+dwNgVnVG1FeoCWRR9zmptXYYgfkLBKer+HHZk+84xcFD4ACkCo4b+UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:20:36.964845Z"},"content_sha256":"42a149792c62147c22cbf74ba1a0c53b6e6526f726df0eff700ffcb00fc362cc","schema_version":"1.0","event_id":"sha256:42a149792c62147c22cbf74ba1a0c53b6e6526f726df0eff700ffcb00fc362cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ATJC6J6UTZOT6G5BGSQW3Y4S4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical reconstruction and forcing absoluteness of standard structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.LO","authors_text":"Tomasz Kania","submitted_at":"2026-06-01T21:12:34Z","abstract_excerpt":"We isolate a simple preservation principle governing when it is absolute, between transitive models of set theory, that a given algebraic or topological-algebraic structure has a standard form $F(X)$ indexed by a set $X$. The principle is: if the index $X$ (or a proxy for it) can be recovered from $F(X)$ by a uniform definable construction, then the class of structures isomorphic to some~$F(X)$ is downward absolute from forcing extensions. Answering a question raised by Noah Schweber, we deduce in particular that no group that fails to be a full symmetric group in the ground model can become o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02898","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/2606.02898/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":"2026-06-03T01:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doHFAG5JL2rRr65u4VnSWtESu6iz1DryhsfKQNp1vi/g3UtntN88+IoI8KU2hpKBQg355Gr+bT/X6sCx8EioCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T17:20:36.965609Z"},"content_sha256":"00b824f6e8f8116b2d80c7af39c81755d69ac1a9cc86bc1aba77ad1e48c839da","schema_version":"1.0","event_id":"sha256:00b824f6e8f8116b2d80c7af39c81755d69ac1a9cc86bc1aba77ad1e48c839da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/bundle.json","state_url":"https://pith.science/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/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":"2026-06-11T17:20:36Z","links":{"resolver":"https://pith.science/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I","bundle":"https://pith.science/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/bundle.json","state":"https://pith.science/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATJC6J6UTZOT6G5BGSQW3Y4S4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ATJC6J6UTZOT6G5BGSQW3Y4S4I","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":"519d85313c19ea9c7b06ecab96d2ba220bffab9109f58ab195d045725dc45321","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T21:12:34Z","title_canon_sha256":"b86fe640c6b356efb856d5b24feca10b892da9184ab0de01c18fd50d0fcf41a5"},"schema_version":"1.0","source":{"id":"2606.02898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02898","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02898v1","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02898","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"ATJC6J6UTZOT","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"ATJC6J6UTZOT6G5B","created_at":"2026-06-03T01:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"ATJC6J6U","created_at":"2026-06-03T01:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:00b824f6e8f8116b2d80c7af39c81755d69ac1a9cc86bc1aba77ad1e48c839da","target":"graph","created_at":"2026-06-03T01:05:25Z","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/2606.02898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We isolate a simple preservation principle governing when it is absolute, between transitive models of set theory, that a given algebraic or topological-algebraic structure has a standard form $F(X)$ indexed by a set $X$. The principle is: if the index $X$ (or a proxy for it) can be recovered from $F(X)$ by a uniform definable construction, then the class of structures isomorphic to some~$F(X)$ is downward absolute from forcing extensions. Answering a question raised by Noah Schweber, we deduce in particular that no group that fails to be a full symmetric group in the ground model can become o","authors_text":"Tomasz Kania","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T21:12:34Z","title":"Canonical reconstruction and forcing absoluteness of standard structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02898","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":"sha256:42a149792c62147c22cbf74ba1a0c53b6e6526f726df0eff700ffcb00fc362cc","target":"record","created_at":"2026-06-03T01:05:25Z","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":"519d85313c19ea9c7b06ecab96d2ba220bffab9109f58ab195d045725dc45321","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T21:12:34Z","title_canon_sha256":"b86fe640c6b356efb856d5b24feca10b892da9184ab0de01c18fd50d0fcf41a5"},"schema_version":"1.0","source":{"id":"2606.02898","kind":"arxiv","version":1}},"canonical_sha256":"04d22f27d49e5d3f1ba134a16de392e20bca2c70267aa610f493dc7f269c1238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04d22f27d49e5d3f1ba134a16de392e20bca2c70267aa610f493dc7f269c1238","first_computed_at":"2026-06-03T01:05:25.972810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:25.972810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBIUokd0RUwDkRtXW1uwLOQchUBnN9Hd0iYT2nS7DDynPt6HSDl1mvmVxbzd6diAfaCJRu2tc3ulFrrQ95aTCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:25.973223Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42a149792c62147c22cbf74ba1a0c53b6e6526f726df0eff700ffcb00fc362cc","sha256:00b824f6e8f8116b2d80c7af39c81755d69ac1a9cc86bc1aba77ad1e48c839da"],"state_sha256":"53b35147bf877d21380ad1326d88c3a755dd139736edf3355b677a8b617ed547"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4hvqoThQ7WQM1s0N8Z4tveo0jZ0Htq+d572+vi4IcvB4G6s9JyxeBwiRntuaq76cmnnKcEI/FD3Uku+1W3m2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T17:20:36.970108Z","bundle_sha256":"4fe47103beae82cfaedce2cadf7a5ce4fbccaa7a59a2879ce05532c371aa3232"}}