{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_2b2fe56253952ea10c8efd6417a25c25727fcf587451b08d25336e0ceb250eb1","bitcoin_anchor":{"bitcoin_attestations":["bitcoin_block_949451"],"calendar_attestations":["https://finney.calendar.eternitywall.com","https://btc.calendar.catallaxy.com","https://alice.btc.calendar.opentimestamps.org","https://bob.btc.calendar.opentimestamps.org"],"ots_url":"/registry/data/substrate/anchors/77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3.ots","stamped_at":"2026-05-15T03:00:03Z","status":"bitcoin"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_2b2fe56253952ea10c8efd6417a25c25727fcf587451b08d25336e0ceb250eb1","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"9e4ce1420ee43dc83c03c6b1f51beb1092af3807c6f1e0d84b9a9ece34b1d289","published":"Thu, 14 May 2026 00:00:00 -0400","receipt_hash":"9e4ce1420ee43dc83c03c6b1f51beb1092af3807c6f1e0d84b9a9ece34b1d289","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"9e4ce1420ee43dc83c03c6b1f51beb1092af3807c6f1e0d84b9a9ece34b1d289","observed_at":"2026-05-14T04:43:36.462865Z","parent_run_hash":"eb105e641aec4518c665fb1a0f748c2a8c8189675990bd4092425661eb7af1d8","published":"Thu, 14 May 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2605.12968v1 Announce Type: cross \nAbstract: Do large language models internally encode ontological relations in a formally verifiable algebraic structure? We introduce Algebraic Ontology Projection (AOP), which projects LLM hidden states into the Galois Field F2 under Liskov Substitution Principle constraints, using only 42 relational pairs as algebraic keys. AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone.\n  This algebraic structure is strongly layer-dependent. We introduce Semantic Crystallisation (SC), a metric that quantifies F2 constraint satisfaction relative to a random baseline and predicts zero-shot accuracy without held-out data. System prompts act as algebraic boundary conditions: only their combination with instruction tuning prevents Late-layer Collapse -- a systematic degra","title":"Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2","url":"https://arxiv.org/abs/2605.12968","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.12968v1 Announce Type: cross \nAbstract: Do large language models internally encode ontological relations in a formally verifiable algebraic structure? We introduce Algebraic Ontology Projection (AOP), which projects LLM hidden states into the Galois Field F2 under Liskov Substitution Principle constraints, using only 42 relational pairs as algebraic keys. AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone.\n  This algebraic structure is strongly layer-dependent. We introduce Semantic Crystallisation (SC), a metric that quantifies F2 constraint satisfaction relative to a random baseline and predicts zero-shot accuracy without held-out data. System prompts act as algebraic boundary conditions: only their combination with instruction tuning prevents Late-layer Collapse -- a systematic degra","title":"Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-14T04:43:36Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.12968"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d1e113569275ad109eff34e3539a8bb2f424ab9610a24715ac223ce4b6189f33fdf7c365890917b9dacd6dda7c2710940effd83765f5be80e56114afb886ae09","signer":"crovia.substrate","subject":{"observed_at":"2026-05-14T04:43:36Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.12968"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"eb111e15f155089b660f5ba281548737e5e906e6a5338e78899219826fe452f2","leaf_index":132570,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"684d8dbd377944636f565864246c4a5e065a305f1a04b41fc02849444887780a","side":"right"},{"sibling":"a857633df338b03c6426e7535a302d4112a15345944d739b60c274d31d6bab0f","side":"left"},{"sibling":"f44577be1783c5158cfe4056b55e439cb84bec6c64bdd19832496d222ca390cb","side":"right"},{"sibling":"9e0e9a4bcec99239a2b26ff1c5c1bce433e30bba6997a33824c338820b369a4e","side":"left"},{"sibling":"f068c3b6dfe550506abbaa8154bd3d13018b6afddd191747c40432e5e870c543","side":"left"},{"sibling":"b73ae76f14bffb2d8b88fbea95caf35a45c2c7a4bdab30329c97fbcdcbd21dd6","side":"right"},{"sibling":"5c93e75b7ee6b7c15dd4ccfeb2ad5773606f9e202ac37c66e6cfe32ca75f287f","side":"left"},{"sibling":"5481966fbd92dc66ec8b3fff9fc4dcddbff0f35b3e0cafc74158f753d7858d6b","side":"left"},{"sibling":"ed110cac74740161e005dcd47c35637ac99ecf93121b3961837570c3af56caa0","side":"left"},{"sibling":"2270188e7d95b52d2bade0ab7da2d0816592f30757dcf71636f21b8f46eb1317","side":"right"},{"sibling":"c03f0a468f574a08ffe8b17e1a17bd88216e1359f0e33a54447e160cd8675da0","side":"left"},{"sibling":"038ff12da6f55509125ef0d96e1e57dda29a2fe63bf03fba2af4cf7cbcd88b36","side":"right"},{"sibling":"b0419206fe62ef216df3900ca93cffd44df267435a4643dda354c1310079cf91","side":"right"},{"sibling":"0d4a9c03674f9d0ce64df15c15e9f656a54b41f93c428aac8e615fda26291956","side":"right"},{"sibling":"7856d920f3f1f1d2194c1ed7351bf0d674440df3cb423a6911f89cb3e9578c0b","side":"right"},{"sibling":"6ac6396bdd2e9df315427a46155531476e7f9012b4bd962e0d2d6d1209b11723","side":"right"},{"sibling":"7c8dc85cbfe43e19ac759ad176cfa11dba2467ae17927c471d5c55663c4f490d","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_2b2fe56253952ea10c8efd6417a25c25727fcf587451b08d25336e0ceb250eb1"}}