{"_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_42072eb0c4e449b3a5ee10c67cadbaff75e203d47d225cb34a65262c938ee3c2","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_42072eb0c4e449b3a5ee10c67cadbaff75e203d47d225cb34a65262c938ee3c2","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"0ef0ad03167c1d30f9a550372c14e663cd6e472682ae827c5244314360111332","published":"Fri, 29 May 2026 00:00:00 -0400","receipt_hash":"0ef0ad03167c1d30f9a550372c14e663cd6e472682ae827c5244314360111332","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":"0ef0ad03167c1d30f9a550372c14e663cd6e472682ae827c5244314360111332","observed_at":"2026-05-29T04:43:58.478092Z","parent_run_hash":"0fcd87efcfe67ccb9952f747541debc16793919a4d20fd71ca0ad5516a0a13ee","published":"Fri, 29 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:2605.29151v1 Announce Type: cross \nAbstract: We prove real-rootedness for the Poincar\\'e polynomial \\[\n  P_n(t)=\\sum_{i=0}^{n-3} \\dim H^{2i}(\\overline{\\mathcal M}_{0,n};\\mathbb{Q})t^i \\] of the Deligne--Mumford moduli space $\\overline{\\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli. The proof starts from the Keel--Manin--Getzler recurrence, but its main new idea is a bivariate deformation $F_m(y,t)$ of the Poincar\\'e polynomial. This deformation reveals a hidden interlacing structure not visible in the one-variable recurrence. For fixed $t<0$, the zero set of $F_m$ in the $y$-direction is controlled by a Sturm--Rolle argument on the interval $0<y<1-t$. The original polynomial is recovered on the slice $y=1$, and the ordered crossings of the moving roots through this slice give both real-rootedness and strict interlacing. Consequently, the Betti numbers of $\\overline{\\mathcal M}_{0,n}$ form an ultra-log-concave sequence.\n  W","title":"Real-rootedness of the Poincar\\'e polynomials of $\\overline{\\mathcal M}_{0,n}$: an AI-assisted proof","url":"https://arxiv.org/abs/2605.29151","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.29151v1 Announce Type: cross \nAbstract: We prove real-rootedness for the Poincar\\'e polynomial \\[\n  P_n(t)=\\sum_{i=0}^{n-3} \\dim H^{2i}(\\overline{\\mathcal M}_{0,n};\\mathbb{Q})t^i \\] of the Deligne--Mumford moduli space $\\overline{\\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli. The proof starts from the Keel--Manin--Getzler recurrence, but its main new idea is a bivariate deformation $F_m(y,t)$ of the Poincar\\'e polynomial. This deformation reveals a hidden interlacing structure not visible in the one-variable recurrence. For fixed $t<0$, the zero set of $F_m$ in the $y$-direction is controlled by a Sturm--Rolle argument on the interval $0<y<1-t$. The original polynomial is recovered on the slice $y=1$, and the ordered crossings of the moving roots through this slice give both real-rootedness and strict interlacing. Consequently, the Betti numbers of $\\overline{\\mathcal M}_{0,n}$ form an ultra-log-concave sequence.\n  W","title":"Real-rootedness of the Poincar\\'e polynomials of $\\overline{\\mathcal M}_{0,n}$: an AI-assisted proof","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-29T04:43:58Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.29151"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:87d8b72852cb2fb1ffbea1b15e9aec89133ac6b08fa90f2b32ca79420818b4d8fec7a49c288178ec43b80c8242864b67d89f87cda2f9560296183a06241f200e","signer":"crovia.substrate","subject":{"observed_at":"2026-05-29T04:43:58Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.29151"},"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":"5166f64da67930a5179b461d0ca4a91cfebb712135d21d5c2d7f07ad6db35b85","leaf_index":157835,"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":"6a0fd30814469e37beef13d806a78727a3e59ea5fe0ee5d16e74b67c1dbabcee","side":"left"},{"sibling":"dba36c91adc2325c909a379c9cdbfc5c4a0f6972a24a3b738cb0ef6076eb2afd","side":"left"},{"sibling":"73172935d8aa97a6216a102e53d1538750ea5f8468975d9c238a05d144b2e727","side":"right"},{"sibling":"4fad40c77e7c1fe31e6c0ad5875bb44daa131f0ef54916fa4a99a39bae3bf1e7","side":"left"},{"sibling":"9c6454fd53e380a5f22da0b3afb51cc8b84dcd96c90a3c2a9afee24ca88d0a40","side":"right"},{"sibling":"69344f6db47c59a180cb674d3058e5b5d558cd678f50b5fb0fad0eeafe20a300","side":"right"},{"sibling":"baa03d8bd5455a8ed912b06e1971d4d9eda400ea2182069710ca2d118b3ea305","side":"right"},{"sibling":"8fe4932bfd0d62d46f26dbb29e67a452b7b1c018843a618ec931b6043bac464c","side":"left"},{"sibling":"291a37d6414d385e45486ef4725ce7087043d900d04f90b309d04bd876c338e5","side":"right"},{"sibling":"1dcc44e23fbb0218b13591e4b584eca3600dcf365769cb741e0ecd33b25b8c56","side":"right"},{"sibling":"fcf16a6f44025801f5b83e928acce764352ddbc06ae3043d8cde9a409933e6d8","side":"right"},{"sibling":"78982294dee68f9db9288c64d7e507c7865fda96e1b6f7ccff5c8bb152e93c49","side":"left"},{"sibling":"995b421824624a8282c7f44e64c64ee35344800f477ae1845b41be14d3fab94c","side":"right"},{"sibling":"66331bac84ca0f8983eb09fac7eaf95af234f1b82680b793eabff4ee25caac40","side":"left"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"eef0e8906a749d3470f89beeedc723f37a5737010bbb0dcc7cf91515338e5a3e","side":"right"},{"sibling":"1a07e481a9407d71aad078ce854cdeee362163c887fe10f889b0ecf0b5e749ad","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":158251,"merkle_root":"485e6b31fe60c8beba5b394808c7e4c32448b2ff65c2482c480ca0e2a2eda718","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260529T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-29T05:37:37Z","sig_algorithm":"ed25519","signature":"bbf9f005201182fce4f9d94c7a9d01a508b56daf7d9611bd73514f5f616bc059d0e5e1f2edfc95716e6fe08ef5fae38b558cbf7f2fd8f9d5dfe4c34a54c83005","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_42072eb0c4e449b3a5ee10c67cadbaff75e203d47d225cb34a65262c938ee3c2"}}