{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GCFGTTYLO36KBBG2MO2ZOOADGB","short_pith_number":"pith:GCFGTTYL","canonical_record":{"source":{"id":"1310.8147","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T13:27:45Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"845c817496c058aa3517ff12fb8d62e14d472d14beb49e80429fa85905c865e9","abstract_canon_sha256":"a2ec4c58979905c5b6c2970c4e4bb524db369d0771cddbeba7cb1a569698dbc2"},"schema_version":"1.0"},"canonical_sha256":"308a69cf0b76fca084da63b59738033075d7dccd29ee81add26e47f0f7836bed","source":{"kind":"arxiv","id":"1310.8147","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8147","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8147v3","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8147","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"GCFGTTYLO36K","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GCFGTTYLO36KBBG2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GCFGTTYL","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GCFGTTYLO36KBBG2MO2ZOOADGB","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8147","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T13:27:45Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"845c817496c058aa3517ff12fb8d62e14d472d14beb49e80429fa85905c865e9","abstract_canon_sha256":"a2ec4c58979905c5b6c2970c4e4bb524db369d0771cddbeba7cb1a569698dbc2"},"schema_version":"1.0"},"canonical_sha256":"308a69cf0b76fca084da63b59738033075d7dccd29ee81add26e47f0f7836bed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:19.106772Z","signature_b64":"MuGGFcVLCE8wfCA40fVrB5r0ybTBVWuiScC7FLDGFcT1chsgztE2n64k0/pcDqv1OOTcMVSuo3xJigr3sbtgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308a69cf0b76fca084da63b59738033075d7dccd29ee81add26e47f0f7836bed","last_reissued_at":"2026-05-18T01:26:19.106189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:19.106189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8147","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":"2026-05-18T01:26:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPuNg5doK+sZtbUoAlm5nsin5DnHoQdd54jUC4gI8ml8bdHYRRq9sbjIGtOrqxhNrGUgC2/1p+3k2R46QsQbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:40:33.994257Z"},"content_sha256":"dfe1cb8de251c28ab30e85b81697cd1c7a85496e391eb95de588f1b855871a2c","schema_version":"1.0","event_id":"sha256:dfe1cb8de251c28ab30e85b81697cd1c7a85496e391eb95de588f1b855871a2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GCFGTTYLO36KBBG2MO2ZOOADGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant measures via inverse limits of finite structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.LO","authors_text":"Cameron Freer, Jaroslav Nesetril, Nathanael Ackerman, Rehana Patel","submitted_at":"2013-10-30T13:27:45Z","abstract_excerpt":"Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are invariant under all permutations of the underlying set that fix all constants. These measures are constructed from inverse limits of measures on certain finite structures. We use this construction to obtain invariant probability measures concentrated on the classes of countable models of certain first-order theories, including measures that do not assign positive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8147","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":"2026-05-18T01:26:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gd9fe9vHqEfjF3C/TTsQYQ36Rb28oQ4zEn/JfnIbxRRfyRA/2sRgWs+PpZPzGj2kZTRGJKGhmc0YBSXyj6y/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:40:33.994645Z"},"content_sha256":"16437617ca4a01e43cafd6a6de310216fbc0695938b29b4cc098ceec62dd5858","schema_version":"1.0","event_id":"sha256:16437617ca4a01e43cafd6a6de310216fbc0695938b29b4cc098ceec62dd5858"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/bundle.json","state_url":"https://pith.science/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/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":"2026-06-22T22:40:33Z","links":{"resolver":"https://pith.science/pith/GCFGTTYLO36KBBG2MO2ZOOADGB","bundle":"https://pith.science/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/bundle.json","state":"https://pith.science/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCFGTTYLO36KBBG2MO2ZOOADGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GCFGTTYLO36KBBG2MO2ZOOADGB","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":"a2ec4c58979905c5b6c2970c4e4bb524db369d0771cddbeba7cb1a569698dbc2","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T13:27:45Z","title_canon_sha256":"845c817496c058aa3517ff12fb8d62e14d472d14beb49e80429fa85905c865e9"},"schema_version":"1.0","source":{"id":"1310.8147","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8147","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8147v3","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8147","created_at":"2026-05-18T01:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"GCFGTTYLO36K","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GCFGTTYLO36KBBG2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GCFGTTYL","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:16437617ca4a01e43cafd6a6de310216fbc0695938b29b4cc098ceec62dd5858","target":"graph","created_at":"2026-05-18T01:26:19Z","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":"Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are invariant under all permutations of the underlying set that fix all constants. These measures are constructed from inverse limits of measures on certain finite structures. We use this construction to obtain invariant probability measures concentrated on the classes of countable models of certain first-order theories, including measures that do not assign positive ","authors_text":"Cameron Freer, Jaroslav Nesetril, Nathanael Ackerman, Rehana Patel","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T13:27:45Z","title":"Invariant measures via inverse limits of finite structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8147","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:dfe1cb8de251c28ab30e85b81697cd1c7a85496e391eb95de588f1b855871a2c","target":"record","created_at":"2026-05-18T01:26:19Z","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":"a2ec4c58979905c5b6c2970c4e4bb524db369d0771cddbeba7cb1a569698dbc2","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T13:27:45Z","title_canon_sha256":"845c817496c058aa3517ff12fb8d62e14d472d14beb49e80429fa85905c865e9"},"schema_version":"1.0","source":{"id":"1310.8147","kind":"arxiv","version":3}},"canonical_sha256":"308a69cf0b76fca084da63b59738033075d7dccd29ee81add26e47f0f7836bed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"308a69cf0b76fca084da63b59738033075d7dccd29ee81add26e47f0f7836bed","first_computed_at":"2026-05-18T01:26:19.106189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:19.106189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MuGGFcVLCE8wfCA40fVrB5r0ybTBVWuiScC7FLDGFcT1chsgztE2n64k0/pcDqv1OOTcMVSuo3xJigr3sbtgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:19.106772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8147","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfe1cb8de251c28ab30e85b81697cd1c7a85496e391eb95de588f1b855871a2c","sha256:16437617ca4a01e43cafd6a6de310216fbc0695938b29b4cc098ceec62dd5858"],"state_sha256":"5a3d58763df407f1b1b333382936520f6dd3c6770c33796d2d332cd119c1649b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQu802cC6R8ZNlnThnM0kjHSaqVC4/5/rOyuM64Z8EI6JBWQVFl/QwgV9SzaIgNdYmX4HYI3nQoH1b3XQNssDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:40:33.996643Z","bundle_sha256":"42d7009a01e34eaaf65bb69f909dc90c1b7337ae426a31b433db1f1cc8ebf979"}}