{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NRP42U5WNH3FST3XHBQFFM7L6R","short_pith_number":"pith:NRP42U5W","canonical_record":{"source":{"id":"2605.25271","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-24T21:56:27Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"979b5752b486a1b081a4fd9e5b69738c84b4d96a4f0896db34152971100d16c6","abstract_canon_sha256":"61a695a481aa12661b6200a6334c24bc0a1a2394e0a9f94bfce635ce77ece7cc"},"schema_version":"1.0"},"canonical_sha256":"6c5fcd53b669f6594f77386052b3ebf448b9d2dafc8ee0f46302f44f84f354d2","source":{"kind":"arxiv","id":"2605.25271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25271","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25271v1","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25271","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"NRP42U5WNH3F","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_16","alias_value":"NRP42U5WNH3FST3X","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_8","alias_value":"NRP42U5W","created_at":"2026-05-26T02:04:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NRP42U5WNH3FST3XHBQFFM7L6R","target":"record","payload":{"canonical_record":{"source":{"id":"2605.25271","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-24T21:56:27Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"979b5752b486a1b081a4fd9e5b69738c84b4d96a4f0896db34152971100d16c6","abstract_canon_sha256":"61a695a481aa12661b6200a6334c24bc0a1a2394e0a9f94bfce635ce77ece7cc"},"schema_version":"1.0"},"canonical_sha256":"6c5fcd53b669f6594f77386052b3ebf448b9d2dafc8ee0f46302f44f84f354d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:26.623891Z","signature_b64":"qgdcqLC7n5imk4t7tJoc1YAZ8pIjUba+X/eeI76AS75aCxZsUOh7UJNcGtz4+oENpKP2/Ucluc+3mFGMS8jdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c5fcd53b669f6594f77386052b3ebf448b9d2dafc8ee0f46302f44f84f354d2","last_reissued_at":"2026-05-26T02:04:26.623205Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:26.623205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.25271","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":"2026-05-26T02:04:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQrUPVSCGPDIlgPPT8yxYsfhJsXivLAxPGAeMLzaFE++vNmDjsmF+iRnutgxfGjXSUrkZ56ennML6UvJgC8JDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:38:19.338392Z"},"content_sha256":"302fc74d56dfc2c8a648e8569212b8bd4f669030b35bf3e37f1f4d208a611aee","schema_version":"1.0","event_id":"sha256:302fc74d56dfc2c8a648e8569212b8bd4f669030b35bf3e37f1f4d208a611aee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NRP42U5WNH3FST3XHBQFFM7L6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"math.AG","authors_text":"Gergely B\\'erczi, L\\'aszl\\'o M. Feh\\'er","submitted_at":"2026-05-24T21:56:27Z","abstract_excerpt":"We study the symmetric polynomial $\\prod_{\\alpha\\in A_{n,d}}\\bigl(1+\\alpha_1 x_1+\\cdots+\\alpha_n x_n\\bigr)$ where $A_{n,d}:=\\{\\alpha\\in\\mathbb{Z}_{\\ge 0}^n:|\\alpha|=d\\}$, which is the total Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$, viewed as a torus representation whose Chern roots are the weights $\\alpha_1 x_1+\\cdots+\\alpha_n x_n$ for $\\alpha\\in A_{n,d}$. Its homogeneous degree-$k$ part $c_k(n,d)$ is the $k$-th Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$. These Chern classes, together with their coefficients in various symmetric function bases, play a central role in enumerative geomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25271","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/2605.25271/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":"2026-05-26T02:04:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Trvn8a0J4B/kGC+7o5ysgh+nnsRhZcGxSRXpVtjjLbgL1Wn35GxXMff7tQZRH9o/7qgbO+y5cNV/AiVanWGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:38:19.339043Z"},"content_sha256":"f6bfbae19d4dd1d322e7f4a9e9b043adfd15b0e3cd9be454cbcff4e5d43c6368","schema_version":"1.0","event_id":"sha256:f6bfbae19d4dd1d322e7f4a9e9b043adfd15b0e3cd9be454cbcff4e5d43c6368"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRP42U5WNH3FST3XHBQFFM7L6R/bundle.json","state_url":"https://pith.science/pith/NRP42U5WNH3FST3XHBQFFM7L6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRP42U5WNH3FST3XHBQFFM7L6R/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":"2026-06-07T12:38:19Z","links":{"resolver":"https://pith.science/pith/NRP42U5WNH3FST3XHBQFFM7L6R","bundle":"https://pith.science/pith/NRP42U5WNH3FST3XHBQFFM7L6R/bundle.json","state":"https://pith.science/pith/NRP42U5WNH3FST3XHBQFFM7L6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRP42U5WNH3FST3XHBQFFM7L6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NRP42U5WNH3FST3XHBQFFM7L6R","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":"61a695a481aa12661b6200a6334c24bc0a1a2394e0a9f94bfce635ce77ece7cc","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-24T21:56:27Z","title_canon_sha256":"979b5752b486a1b081a4fd9e5b69738c84b4d96a4f0896db34152971100d16c6"},"schema_version":"1.0","source":{"id":"2605.25271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25271","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25271v1","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25271","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"NRP42U5WNH3F","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_16","alias_value":"NRP42U5WNH3FST3X","created_at":"2026-05-26T02:04:26Z"},{"alias_kind":"pith_short_8","alias_value":"NRP42U5W","created_at":"2026-05-26T02:04:26Z"}],"graph_snapshots":[{"event_id":"sha256:f6bfbae19d4dd1d322e7f4a9e9b043adfd15b0e3cd9be454cbcff4e5d43c6368","target":"graph","created_at":"2026-05-26T02:04:26Z","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/2605.25271/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the symmetric polynomial $\\prod_{\\alpha\\in A_{n,d}}\\bigl(1+\\alpha_1 x_1+\\cdots+\\alpha_n x_n\\bigr)$ where $A_{n,d}:=\\{\\alpha\\in\\mathbb{Z}_{\\ge 0}^n:|\\alpha|=d\\}$, which is the total Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$, viewed as a torus representation whose Chern roots are the weights $\\alpha_1 x_1+\\cdots+\\alpha_n x_n$ for $\\alpha\\in A_{n,d}$. Its homogeneous degree-$k$ part $c_k(n,d)$ is the $k$-th Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$. These Chern classes, together with their coefficients in various symmetric function bases, play a central role in enumerative geomet","authors_text":"Gergely B\\'erczi, L\\'aszl\\'o M. Feh\\'er","cross_cats":["cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-24T21:56:27Z","title":"Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25271","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":"sha256:302fc74d56dfc2c8a648e8569212b8bd4f669030b35bf3e37f1f4d208a611aee","target":"record","created_at":"2026-05-26T02:04:26Z","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":"61a695a481aa12661b6200a6334c24bc0a1a2394e0a9f94bfce635ce77ece7cc","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-24T21:56:27Z","title_canon_sha256":"979b5752b486a1b081a4fd9e5b69738c84b4d96a4f0896db34152971100d16c6"},"schema_version":"1.0","source":{"id":"2605.25271","kind":"arxiv","version":1}},"canonical_sha256":"6c5fcd53b669f6594f77386052b3ebf448b9d2dafc8ee0f46302f44f84f354d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c5fcd53b669f6594f77386052b3ebf448b9d2dafc8ee0f46302f44f84f354d2","first_computed_at":"2026-05-26T02:04:26.623205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:26.623205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qgdcqLC7n5imk4t7tJoc1YAZ8pIjUba+X/eeI76AS75aCxZsUOh7UJNcGtz4+oENpKP2/Ucluc+3mFGMS8jdCA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:26.623891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:302fc74d56dfc2c8a648e8569212b8bd4f669030b35bf3e37f1f4d208a611aee","sha256:f6bfbae19d4dd1d322e7f4a9e9b043adfd15b0e3cd9be454cbcff4e5d43c6368"],"state_sha256":"3f40d6ab36c9a2eaa70b80f66fe47e75934c84f1e16bbc49786bf2418082cd3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iE40whF5TYWAvYUjmr/ffaNKtGJmxNdXmShJU10XrOAQcvBVAuJrtGYz2mLMtU75XjpWYPg4/KhxY4TPgRmHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:38:19.343197Z","bundle_sha256":"5911aee11511db382479fa8b671df7071c4f2a4862557b6c7e9b2a0df5720a89"}}