{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WJUMPWMB5E33CU7VPFTTFKQQON","short_pith_number":"pith:WJUMPWMB","canonical_record":{"source":{"id":"2509.09455","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-11T13:40:40Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"53ee34d9ace6dc8e4fb9d93e4a7c6b702dbc942f4b9bc742b457cebd4ab4cd01","abstract_canon_sha256":"024be2cfe689a80a850c94cf73be691a8a299eda010302927795b90936270918"},"schema_version":"1.0"},"canonical_sha256":"b268c7d981e937b153f5796732aa1073591e1f14ae3365ae23c71f068069c48a","source":{"kind":"arxiv","id":"2509.09455","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09455","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09455v8","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09455","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"WJUMPWMB5E33","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_16","alias_value":"WJUMPWMB5E33CU7V","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_8","alias_value":"WJUMPWMB","created_at":"2026-06-02T03:04:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WJUMPWMB5E33CU7VPFTTFKQQON","target":"record","payload":{"canonical_record":{"source":{"id":"2509.09455","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-11T13:40:40Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"53ee34d9ace6dc8e4fb9d93e4a7c6b702dbc942f4b9bc742b457cebd4ab4cd01","abstract_canon_sha256":"024be2cfe689a80a850c94cf73be691a8a299eda010302927795b90936270918"},"schema_version":"1.0"},"canonical_sha256":"b268c7d981e937b153f5796732aa1073591e1f14ae3365ae23c71f068069c48a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:34.156954Z","signature_b64":"hwj13rGB9xxhK/WF9jsR9c43VEGoiNwO9Xt8e6JWyT1omlanBV/VHrn7snlPjJQwGAEFm+1ZdahipIWgTqZ1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b268c7d981e937b153f5796732aa1073591e1f14ae3365ae23c71f068069c48a","last_reissued_at":"2026-06-02T03:04:34.156537Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:34.156537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.09455","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYFIjQJQ8IZ0s/lTdKS9ZyErCgZSU8SCwFQ782hfUk7pl9gABn6eRWqH4gAdvSF4n7keX3D6NEetwB6+XaHOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:04:00.978070Z"},"content_sha256":"a1083f400a705eced410d9d3917f86fc8788d2ab8f25586a302baed9116cc828","schema_version":"1.0","event_id":"sha256:a1083f400a705eced410d9d3917f86fc8788d2ab8f25586a302baed9116cc828"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WJUMPWMB5E33CU7VPFTTFKQQON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Negation Of Singer's Conjecture For The Sixth Algebraic Transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2025-09-11T13:40:40Z","abstract_excerpt":"Let $\\mathscr A$ be the Steenrod algebra over the field of characteristic two, $\\mathbb F_2.$ Denote by $GL(q)$ the general linear group of rank $q$ over $\\mathbb F_2.$ The algebraic transfer, introduced by W. Singer [Math. Z. 202 (1989), 493-523], is a rather effective tool for unraveling the intricate structure of the (mod-2) cohomology of the Steenrod algebra, ${\\rm Ext}_{\\mathscr A}^{q,*}(\\mathbb F_2, \\mathbb F_2).$ The Kameko homomorphism is one of the useful tools to study the dimension of the domain of the Singer transfer. Singer conjectured that the algebraic transfer is always a monom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09455","kind":"arxiv","version":8},"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/2509.09455/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":"2026-06-02T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icr84PpxZNPm1Y5IUITDuy0cKrfdd4HJLQq0fsD/VBabn/4tIliAyG8bWZjvSQJJq4VZNQm0l6TI0Q0ABa/+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:04:00.978754Z"},"content_sha256":"2be00f2fa3e072cc0211cba6db534cafb97914a2c2f7111d8eb95baff728e03e","schema_version":"1.0","event_id":"sha256:2be00f2fa3e072cc0211cba6db534cafb97914a2c2f7111d8eb95baff728e03e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJUMPWMB5E33CU7VPFTTFKQQON/bundle.json","state_url":"https://pith.science/pith/WJUMPWMB5E33CU7VPFTTFKQQON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJUMPWMB5E33CU7VPFTTFKQQON/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":"2026-06-08T17:04:00Z","links":{"resolver":"https://pith.science/pith/WJUMPWMB5E33CU7VPFTTFKQQON","bundle":"https://pith.science/pith/WJUMPWMB5E33CU7VPFTTFKQQON/bundle.json","state":"https://pith.science/pith/WJUMPWMB5E33CU7VPFTTFKQQON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJUMPWMB5E33CU7VPFTTFKQQON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WJUMPWMB5E33CU7VPFTTFKQQON","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":"024be2cfe689a80a850c94cf73be691a8a299eda010302927795b90936270918","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-11T13:40:40Z","title_canon_sha256":"53ee34d9ace6dc8e4fb9d93e4a7c6b702dbc942f4b9bc742b457cebd4ab4cd01"},"schema_version":"1.0","source":{"id":"2509.09455","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09455","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09455v8","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09455","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"WJUMPWMB5E33","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_16","alias_value":"WJUMPWMB5E33CU7V","created_at":"2026-06-02T03:04:34Z"},{"alias_kind":"pith_short_8","alias_value":"WJUMPWMB","created_at":"2026-06-02T03:04:34Z"}],"graph_snapshots":[{"event_id":"sha256:2be00f2fa3e072cc0211cba6db534cafb97914a2c2f7111d8eb95baff728e03e","target":"graph","created_at":"2026-06-02T03:04:34Z","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/2509.09455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathscr A$ be the Steenrod algebra over the field of characteristic two, $\\mathbb F_2.$ Denote by $GL(q)$ the general linear group of rank $q$ over $\\mathbb F_2.$ The algebraic transfer, introduced by W. Singer [Math. Z. 202 (1989), 493-523], is a rather effective tool for unraveling the intricate structure of the (mod-2) cohomology of the Steenrod algebra, ${\\rm Ext}_{\\mathscr A}^{q,*}(\\mathbb F_2, \\mathbb F_2).$ The Kameko homomorphism is one of the useful tools to study the dimension of the domain of the Singer transfer. Singer conjectured that the algebraic transfer is always a monom","authors_text":"Dang Vo Phuc","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-11T13:40:40Z","title":"The Negation Of Singer's Conjecture For The Sixth Algebraic Transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09455","kind":"arxiv","version":8},"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:a1083f400a705eced410d9d3917f86fc8788d2ab8f25586a302baed9116cc828","target":"record","created_at":"2026-06-02T03:04:34Z","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":"024be2cfe689a80a850c94cf73be691a8a299eda010302927795b90936270918","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-11T13:40:40Z","title_canon_sha256":"53ee34d9ace6dc8e4fb9d93e4a7c6b702dbc942f4b9bc742b457cebd4ab4cd01"},"schema_version":"1.0","source":{"id":"2509.09455","kind":"arxiv","version":8}},"canonical_sha256":"b268c7d981e937b153f5796732aa1073591e1f14ae3365ae23c71f068069c48a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b268c7d981e937b153f5796732aa1073591e1f14ae3365ae23c71f068069c48a","first_computed_at":"2026-06-02T03:04:34.156537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:34.156537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hwj13rGB9xxhK/WF9jsR9c43VEGoiNwO9Xt8e6JWyT1omlanBV/VHrn7snlPjJQwGAEFm+1ZdahipIWgTqZ1Dw==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:34.156954Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.09455","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1083f400a705eced410d9d3917f86fc8788d2ab8f25586a302baed9116cc828","sha256:2be00f2fa3e072cc0211cba6db534cafb97914a2c2f7111d8eb95baff728e03e"],"state_sha256":"7bc55dc0603cdb545160c46210ab5ce411cec180d5af2fefea7455bea45ca874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWVPBWgncjx4b4zWxvKZRwMqNOE6fh83I5P/ou6nZbhU5fBWaWd9bHEcI/8h1aTZDcxlrdiyOujeq6geX+/5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:04:00.981115Z","bundle_sha256":"06717a65e3c6515f3a15e4c51e21b1622a980f386152756895626a16df859f4c"}}