{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VRYY55CXAAUMHTIJFU2UQBAX5C","short_pith_number":"pith:VRYY55CX","canonical_record":{"source":{"id":"2507.10108","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-14T09:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"bc7032d5683e4ec47a44b4273aa80509d4b627e808021372e915845c45793136","abstract_canon_sha256":"759e32899cc30ff148a05138e9e2910f2e7295761e381874318296c9c3e81cf7"},"schema_version":"1.0"},"canonical_sha256":"ac718ef4570028c3cd092d35480417e89c91434a72e8bb62b7c5682fac08b7d8","source":{"kind":"arxiv","id":"2507.10108","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10108","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10108v4","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10108","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_12","alias_value":"VRYY55CXAAUM","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_16","alias_value":"VRYY55CXAAUMHTIJ","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_8","alias_value":"VRYY55CX","created_at":"2026-07-05T11:42:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VRYY55CXAAUMHTIJFU2UQBAX5C","target":"record","payload":{"canonical_record":{"source":{"id":"2507.10108","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-14T09:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"bc7032d5683e4ec47a44b4273aa80509d4b627e808021372e915845c45793136","abstract_canon_sha256":"759e32899cc30ff148a05138e9e2910f2e7295761e381874318296c9c3e81cf7"},"schema_version":"1.0"},"canonical_sha256":"ac718ef4570028c3cd092d35480417e89c91434a72e8bb62b7c5682fac08b7d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:55.189717Z","signature_b64":"QOqynVIcdq+0ySJ+h4za1p6rxGUKG1YKyvd4yEKaSSEtpCDabtClnpUip1lvWeQqGiCsAvD2ysFCOgJiH82/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac718ef4570028c3cd092d35480417e89c91434a72e8bb62b7c5682fac08b7d8","last_reissued_at":"2026-07-05T11:42:55.189122Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:55.189122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.10108","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:42:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTtzmBYG2hMwhprbnaQcR0kexxDYtOHxHnp/kS3QSGQWgBfjKTFU7uHvP/jHEFRa1kOUUeaTJUxCy+4jgTpTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:31:51.624833Z"},"content_sha256":"cb1686eab82349c9bb9c10ee341370909fa89ce581a4b695181ea5f5a5f83b91","schema_version":"1.0","event_id":"sha256:cb1686eab82349c9bb9c10ee341370909fa89ce581a4b695181ea5f5a5f83b91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VRYY55CXAAUMHTIJFU2UQBAX5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Approaches to the Singer Transfer: Preimages in the Lambda Algebra and $G_k$-Invariant Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2025-07-14T09:47:58Z","abstract_excerpt":"We present a systematic, algorithmic method to compute the preimage of elements under the Singer algebraic transfer. Using the lambda algebra and the invariant-theoretic formula of P.H. Chon and L.M. Ha [5], we formulate the preimage search as a solvable problem in linear algebra. This framework is applied to study key indecomposable elements in the Adams spectral sequence. As a consequence, we show that the proof of the known result that the indecomposable element $d_0 \\in \\mathrm{Ext}^{4,18}_{\\mathcal A}(\\mathbb Z/2, \\mathbb Z/2).$ lies in the image of the fourth Singer transfer, as given by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10108","kind":"arxiv","version":4},"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/2507.10108/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":"2026-07-05T11:42:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y84LsiMCYn8en9iWQ17SIL5yXHx7uODu7YXgIV6lItuq1s+gOuU4rH1R3Bu9vI0wt1+scWPVujobE/njGOcCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:31:51.625328Z"},"content_sha256":"28f4f87d86fa907792a5f2acfd61ec532aea20f3449e799bdbd7650054506ba4","schema_version":"1.0","event_id":"sha256:28f4f87d86fa907792a5f2acfd61ec532aea20f3449e799bdbd7650054506ba4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/bundle.json","state_url":"https://pith.science/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/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":"2026-08-05T23:31:51Z","links":{"resolver":"https://pith.science/pith/VRYY55CXAAUMHTIJFU2UQBAX5C","bundle":"https://pith.science/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/bundle.json","state":"https://pith.science/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRYY55CXAAUMHTIJFU2UQBAX5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VRYY55CXAAUMHTIJFU2UQBAX5C","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":"759e32899cc30ff148a05138e9e2910f2e7295761e381874318296c9c3e81cf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-14T09:47:58Z","title_canon_sha256":"bc7032d5683e4ec47a44b4273aa80509d4b627e808021372e915845c45793136"},"schema_version":"1.0","source":{"id":"2507.10108","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10108","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10108v4","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10108","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_12","alias_value":"VRYY55CXAAUM","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_16","alias_value":"VRYY55CXAAUMHTIJ","created_at":"2026-07-05T11:42:55Z"},{"alias_kind":"pith_short_8","alias_value":"VRYY55CX","created_at":"2026-07-05T11:42:55Z"}],"graph_snapshots":[{"event_id":"sha256:28f4f87d86fa907792a5f2acfd61ec532aea20f3449e799bdbd7650054506ba4","target":"graph","created_at":"2026-07-05T11:42:55Z","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/2507.10108/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a systematic, algorithmic method to compute the preimage of elements under the Singer algebraic transfer. Using the lambda algebra and the invariant-theoretic formula of P.H. Chon and L.M. Ha [5], we formulate the preimage search as a solvable problem in linear algebra. This framework is applied to study key indecomposable elements in the Adams spectral sequence. As a consequence, we show that the proof of the known result that the indecomposable element $d_0 \\in \\mathrm{Ext}^{4,18}_{\\mathcal A}(\\mathbb Z/2, \\mathbb Z/2).$ lies in the image of the fourth Singer transfer, as given by","authors_text":"Dang Vo Phuc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-14T09:47:58Z","title":"Computational Approaches to the Singer Transfer: Preimages in the Lambda Algebra and $G_k$-Invariant Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10108","kind":"arxiv","version":4},"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:cb1686eab82349c9bb9c10ee341370909fa89ce581a4b695181ea5f5a5f83b91","target":"record","created_at":"2026-07-05T11:42:55Z","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":"759e32899cc30ff148a05138e9e2910f2e7295761e381874318296c9c3e81cf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-14T09:47:58Z","title_canon_sha256":"bc7032d5683e4ec47a44b4273aa80509d4b627e808021372e915845c45793136"},"schema_version":"1.0","source":{"id":"2507.10108","kind":"arxiv","version":4}},"canonical_sha256":"ac718ef4570028c3cd092d35480417e89c91434a72e8bb62b7c5682fac08b7d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac718ef4570028c3cd092d35480417e89c91434a72e8bb62b7c5682fac08b7d8","first_computed_at":"2026-07-05T11:42:55.189122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:42:55.189122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOqynVIcdq+0ySJ+h4za1p6rxGUKG1YKyvd4yEKaSSEtpCDabtClnpUip1lvWeQqGiCsAvD2ysFCOgJiH82/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:42:55.189717Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.10108","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb1686eab82349c9bb9c10ee341370909fa89ce581a4b695181ea5f5a5f83b91","sha256:28f4f87d86fa907792a5f2acfd61ec532aea20f3449e799bdbd7650054506ba4"],"state_sha256":"c5f906d8e13e2b62e6f72ae9839ba3bfed5f8b4eab25ea82d1e895bdf44eed02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZvnT+twNCSkPgxVzpSdN3vu56DzXlmXTuJ9KOKcbPfuoqWIRSkLot0NjR8X1lS1/E3HybResBct62R7/BTFaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T23:31:51.630076Z","bundle_sha256":"abd5ad8639e3d15b0ce2ae48759dca16f8a6d9885ae7011fb8056c2ff80beedb"}}