{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GDC7SPP3M3WHG7ZIPB4UACHICA","short_pith_number":"pith:GDC7SPP3","canonical_record":{"source":{"id":"2602.00118","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-01-27T12:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"313887902c5e016120a355bfb3b24f80dfe66c6f6667c00b99e4cbfdac199dad","abstract_canon_sha256":"633ac017c10bfe6eda1d65329bd8b8bb8176ccb9f05c50209d97e5b3ea1b4256"},"schema_version":"1.0"},"canonical_sha256":"30c5f93dfb66ec737f2878794008e810100c8fe7132676641a4ebff563b22d02","source":{"kind":"arxiv","id":"2602.00118","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00118","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00118v5","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00118","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_12","alias_value":"GDC7SPP3M3WH","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_16","alias_value":"GDC7SPP3M3WHG7ZI","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_8","alias_value":"GDC7SPP3","created_at":"2026-06-04T01:09:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GDC7SPP3M3WHG7ZIPB4UACHICA","target":"record","payload":{"canonical_record":{"source":{"id":"2602.00118","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-01-27T12:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"313887902c5e016120a355bfb3b24f80dfe66c6f6667c00b99e4cbfdac199dad","abstract_canon_sha256":"633ac017c10bfe6eda1d65329bd8b8bb8176ccb9f05c50209d97e5b3ea1b4256"},"schema_version":"1.0"},"canonical_sha256":"30c5f93dfb66ec737f2878794008e810100c8fe7132676641a4ebff563b22d02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:41.398480Z","signature_b64":"eCnMZ780o5fsObGkhAJEZVt/PvNm5QeOj7TXRIWsAKPXEWCpOv6lN0hSmOlBfUoJOaZ8JrKYJDD8u6CwmaH3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30c5f93dfb66ec737f2878794008e810100c8fe7132676641a4ebff563b22d02","last_reissued_at":"2026-06-04T01:09:41.397834Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:41.397834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.00118","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8i7K9DFU0tbO+kSGK5wQlXSdiM29CsYkGw516ngXdP+uVqH2on0BrMgZnfzYrBBbZu8gg2E0DyFguE7gkIFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:12.417985Z"},"content_sha256":"2cd90e3e8f6515e2e40b620f3990ad51d708c3015e6523c247c7bb13c92379d9","schema_version":"1.0","event_id":"sha256:2cd90e3e8f6515e2e40b620f3990ad51d708c3015e6523c247c7bb13c92379d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GDC7SPP3M3WHG7ZIPB4UACHICA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Structural Characterization of the Hit Image in the Motivic Steenrod Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2026-01-27T12:26:09Z","abstract_excerpt":"The motivic hit problem seeks a minimal set of generators for $H^{*,*}(BV_n; \\mathbb{F}_{2})$ as a module over the mod $2$ motivic Steenrod algebra. Kameko demonstrated the failure of the motivic Peterson conjecture by constructing non-hit monomials $z_k$ in degree $d = k + 2d_1$. His analysis involves a distinguished summand in the quotient $N_n = M_n / (\\tau)$ spanned by monotone translates of $z_k$. In this paper, we isolate the local top-layer content of this summand before quotienting by hit elements. We construct a linear projection $\\vartheta: N_n^{d,*} \\longrightarrow V$ onto the $M_1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00118","kind":"arxiv","version":5},"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/2602.00118/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":"2026-06-04T01:09:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5uuxhrlKrpv2abXM85tqT8z61OHr/Nwz4DblPs3qberavcW8YieX/Q2FFSEniFUaUMuuX7Cob+iKt5vI3jaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:12.418813Z"},"content_sha256":"b72972813352c96b44f95ced58b6b59988054de26f80a15c979f07bbc7e8423b","schema_version":"1.0","event_id":"sha256:b72972813352c96b44f95ced58b6b59988054de26f80a15c979f07bbc7e8423b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/bundle.json","state_url":"https://pith.science/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/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":"2026-06-09T02:19:12Z","links":{"resolver":"https://pith.science/pith/GDC7SPP3M3WHG7ZIPB4UACHICA","bundle":"https://pith.science/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/bundle.json","state":"https://pith.science/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDC7SPP3M3WHG7ZIPB4UACHICA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GDC7SPP3M3WHG7ZIPB4UACHICA","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":"633ac017c10bfe6eda1d65329bd8b8bb8176ccb9f05c50209d97e5b3ea1b4256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-01-27T12:26:09Z","title_canon_sha256":"313887902c5e016120a355bfb3b24f80dfe66c6f6667c00b99e4cbfdac199dad"},"schema_version":"1.0","source":{"id":"2602.00118","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.00118","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"arxiv_version","alias_value":"2602.00118v5","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.00118","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_12","alias_value":"GDC7SPP3M3WH","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_16","alias_value":"GDC7SPP3M3WHG7ZI","created_at":"2026-06-04T01:09:41Z"},{"alias_kind":"pith_short_8","alias_value":"GDC7SPP3","created_at":"2026-06-04T01:09:41Z"}],"graph_snapshots":[{"event_id":"sha256:b72972813352c96b44f95ced58b6b59988054de26f80a15c979f07bbc7e8423b","target":"graph","created_at":"2026-06-04T01:09:41Z","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/2602.00118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The motivic hit problem seeks a minimal set of generators for $H^{*,*}(BV_n; \\mathbb{F}_{2})$ as a module over the mod $2$ motivic Steenrod algebra. Kameko demonstrated the failure of the motivic Peterson conjecture by constructing non-hit monomials $z_k$ in degree $d = k + 2d_1$. His analysis involves a distinguished summand in the quotient $N_n = M_n / (\\tau)$ spanned by monotone translates of $z_k$. In this paper, we isolate the local top-layer content of this summand before quotienting by hit elements. We construct a linear projection $\\vartheta: N_n^{d,*} \\longrightarrow V$ onto the $M_1$","authors_text":"Dang Vo Phuc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-01-27T12:26:09Z","title":"A Structural Characterization of the Hit Image in the Motivic Steenrod Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00118","kind":"arxiv","version":5},"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":"sha256:2cd90e3e8f6515e2e40b620f3990ad51d708c3015e6523c247c7bb13c92379d9","target":"record","created_at":"2026-06-04T01:09:41Z","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":"633ac017c10bfe6eda1d65329bd8b8bb8176ccb9f05c50209d97e5b3ea1b4256","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-01-27T12:26:09Z","title_canon_sha256":"313887902c5e016120a355bfb3b24f80dfe66c6f6667c00b99e4cbfdac199dad"},"schema_version":"1.0","source":{"id":"2602.00118","kind":"arxiv","version":5}},"canonical_sha256":"30c5f93dfb66ec737f2878794008e810100c8fe7132676641a4ebff563b22d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30c5f93dfb66ec737f2878794008e810100c8fe7132676641a4ebff563b22d02","first_computed_at":"2026-06-04T01:09:41.397834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:41.397834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eCnMZ780o5fsObGkhAJEZVt/PvNm5QeOj7TXRIWsAKPXEWCpOv6lN0hSmOlBfUoJOaZ8JrKYJDD8u6CwmaH3AA==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:41.398480Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.00118","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cd90e3e8f6515e2e40b620f3990ad51d708c3015e6523c247c7bb13c92379d9","sha256:b72972813352c96b44f95ced58b6b59988054de26f80a15c979f07bbc7e8423b"],"state_sha256":"ef28c2749a847a3985b59fa676b0f8776b3148a842d2eea969e27238c48dcbe0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Y1VrAsW2ioOIg0f5ZkfRm/n3CdEm30Asrq1nZtycD/Qv5bgAcxc15AM6EX1qBV6gBqtww2mAh9N3vsYovPUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:19:12.423363Z","bundle_sha256":"b542dba2b8aa2b8a4e578edfbd47dda5cd947d2353df4c1df43d15764215f9c7"}}