{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:V55ZPTPXX2PNCNBSQUXX7D2LZA","short_pith_number":"pith:V55ZPTPX","canonical_record":{"source":{"id":"2606.04026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T18:01:01Z","cross_cats_sorted":[],"title_canon_sha256":"0aef5817df686eec2dc0b3eb9b36ae09c431ac5cdbf6aa487d9a586905260180","abstract_canon_sha256":"5300d61006a4e3676fa0bc974e5076c9cf55a16b47542de4abf707c2cc809662"},"schema_version":"1.0"},"canonical_sha256":"af7b97cdf7be9ed13432852f7f8f4bc82c82c66ec4a78d5577467061f1aeabcf","source":{"kind":"arxiv","id":"2606.04026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04026","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04026v1","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04026","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"V55ZPTPXX2PN","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_16","alias_value":"V55ZPTPXX2PNCNBS","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_8","alias_value":"V55ZPTPX","created_at":"2026-06-04T00:06:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:V55ZPTPXX2PNCNBSQUXX7D2LZA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T18:01:01Z","cross_cats_sorted":[],"title_canon_sha256":"0aef5817df686eec2dc0b3eb9b36ae09c431ac5cdbf6aa487d9a586905260180","abstract_canon_sha256":"5300d61006a4e3676fa0bc974e5076c9cf55a16b47542de4abf707c2cc809662"},"schema_version":"1.0"},"canonical_sha256":"af7b97cdf7be9ed13432852f7f8f4bc82c82c66ec4a78d5577467061f1aeabcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T00:06:44.780867Z","signature_b64":"ekzZCVR0BMpEQwgtjCScHGZdPcb9I3dyRAWGihLKFpUi0/0DB80eOmSbYkZu2L6pjuq44W9c/llGKr30jSw5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af7b97cdf7be9ed13432852f7f8f4bc82c82c66ec4a78d5577467061f1aeabcf","last_reissued_at":"2026-06-04T00:06:44.780482Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T00:06:44.780482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04026","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":"2026-06-04T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGhKYobMUnAJoRGSK5z9Iy44XQNS/vNtQgGPPUmxiH+mcxZcOKKiexF9l+h5upSbnasUTLExfCOfx9Z6Xb+yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:42:13.264284Z"},"content_sha256":"bdde3009f01d766b9f850db519b9c6570034bcee513447ab814abba9783fb57a","schema_version":"1.0","event_id":"sha256:bdde3009f01d766b9f850db519b9c6570034bcee513447ab814abba9783fb57a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:V55ZPTPXX2PNCNBSQUXX7D2LZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Visibility Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Frode Alfson Bj{\\o}rdal","submitted_at":"2026-06-01T18:01:01Z","abstract_excerpt":"This paper develops Visibility Theory (VT), a framework in which visibility is taken as the primitive semantic notion and truth is defined in terms of visibility together with a structural condition called step-identity. The theory is formulated in a classical setting and supplied with a revision-theoretic semantics. Visibility theory includes a provability logic KDC, characterized by seriality and confluence and shown to be strongly complete by standard Sahlqvist-theoretic methods.\n  The framework distinguishes between visions, propositions, sets, and truths. Propositions are identified with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04026","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/2606.04026/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":"2026-06-04T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdBm0PVUIVOOw4mfNx0jKNGWkpE/35Ig+zsmG1xxnv6nCGjiJGGrMokdx9h/ZOKuusg5ETrHMKDlFarkQPnXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:42:13.264707Z"},"content_sha256":"31c88f75898f23a1f5017b404f56a5d1abd0b7170d05a031273dc4c01047c3d3","schema_version":"1.0","event_id":"sha256:31c88f75898f23a1f5017b404f56a5d1abd0b7170d05a031273dc4c01047c3d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/bundle.json","state_url":"https://pith.science/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/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":"2026-06-30T23:42:13Z","links":{"resolver":"https://pith.science/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA","bundle":"https://pith.science/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/bundle.json","state":"https://pith.science/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V55ZPTPXX2PNCNBSQUXX7D2LZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:V55ZPTPXX2PNCNBSQUXX7D2LZA","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":"5300d61006a4e3676fa0bc974e5076c9cf55a16b47542de4abf707c2cc809662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T18:01:01Z","title_canon_sha256":"0aef5817df686eec2dc0b3eb9b36ae09c431ac5cdbf6aa487d9a586905260180"},"schema_version":"1.0","source":{"id":"2606.04026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04026","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04026v1","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04026","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"V55ZPTPXX2PN","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_16","alias_value":"V55ZPTPXX2PNCNBS","created_at":"2026-06-04T00:06:44Z"},{"alias_kind":"pith_short_8","alias_value":"V55ZPTPX","created_at":"2026-06-04T00:06:44Z"}],"graph_snapshots":[{"event_id":"sha256:31c88f75898f23a1f5017b404f56a5d1abd0b7170d05a031273dc4c01047c3d3","target":"graph","created_at":"2026-06-04T00:06:44Z","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/2606.04026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops Visibility Theory (VT), a framework in which visibility is taken as the primitive semantic notion and truth is defined in terms of visibility together with a structural condition called step-identity. The theory is formulated in a classical setting and supplied with a revision-theoretic semantics. Visibility theory includes a provability logic KDC, characterized by seriality and confluence and shown to be strongly complete by standard Sahlqvist-theoretic methods.\n  The framework distinguishes between visions, propositions, sets, and truths. Propositions are identified with ","authors_text":"Frode Alfson Bj{\\o}rdal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T18:01:01Z","title":"Visibility Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04026","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:bdde3009f01d766b9f850db519b9c6570034bcee513447ab814abba9783fb57a","target":"record","created_at":"2026-06-04T00:06:44Z","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":"5300d61006a4e3676fa0bc974e5076c9cf55a16b47542de4abf707c2cc809662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-06-01T18:01:01Z","title_canon_sha256":"0aef5817df686eec2dc0b3eb9b36ae09c431ac5cdbf6aa487d9a586905260180"},"schema_version":"1.0","source":{"id":"2606.04026","kind":"arxiv","version":1}},"canonical_sha256":"af7b97cdf7be9ed13432852f7f8f4bc82c82c66ec4a78d5577467061f1aeabcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af7b97cdf7be9ed13432852f7f8f4bc82c82c66ec4a78d5577467061f1aeabcf","first_computed_at":"2026-06-04T00:06:44.780482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T00:06:44.780482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ekzZCVR0BMpEQwgtjCScHGZdPcb9I3dyRAWGihLKFpUi0/0DB80eOmSbYkZu2L6pjuq44W9c/llGKr30jSw5BQ==","signature_status":"signed_v1","signed_at":"2026-06-04T00:06:44.780867Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdde3009f01d766b9f850db519b9c6570034bcee513447ab814abba9783fb57a","sha256:31c88f75898f23a1f5017b404f56a5d1abd0b7170d05a031273dc4c01047c3d3"],"state_sha256":"91e492fad92e9e7bdbd50e90d0feffa6f17173a9516619c911b6e2c30d7300c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mm6Jf5/tgBUTW3CC2uWxCtJQ9VZpFwD2j+e4L8QhWApPd43+5msUtTvSDcscNWrJuaSH8RDMzonRnx13XMooBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:42:13.266790Z","bundle_sha256":"714db4043693e442dc66843655e0e92fcda8b030ff862e24b5d244a7c1690498"}}