{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:3VFYVE4VL742HKPPWTMYB2JRVE","short_pith_number":"pith:3VFYVE4V","canonical_record":{"source":{"id":"0806.3281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-06-19T20:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"b80bf9ac461a707740824b39bbdc05f80e2f820d75a163d51b92f0a5d7fcf082","abstract_canon_sha256":"5828fd5eafbdc1b98f43c79e855bcadeecf6c2ed708e5d6a1a36fb01e14e4f7a"},"schema_version":"1.0"},"canonical_sha256":"dd4b8a93955ff9a3a9efb4d980e931a93ff95962f9ac17b4de469742aef16259","source":{"kind":"arxiv","id":"0806.3281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3281","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3281v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3281","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VFYVE4VL742","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3VFYVE4VL742HKPP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3VFYVE4V","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:3VFYVE4VL742HKPPWTMYB2JRVE","target":"record","payload":{"canonical_record":{"source":{"id":"0806.3281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-06-19T20:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"b80bf9ac461a707740824b39bbdc05f80e2f820d75a163d51b92f0a5d7fcf082","abstract_canon_sha256":"5828fd5eafbdc1b98f43c79e855bcadeecf6c2ed708e5d6a1a36fb01e14e4f7a"},"schema_version":"1.0"},"canonical_sha256":"dd4b8a93955ff9a3a9efb4d980e931a93ff95962f9ac17b4de469742aef16259","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.607785Z","signature_b64":"seS3Sd90Mdr5/Ux9CAGhoSimsXHHDYw5EsV3REuuROPG2vAbkTGc3i0NUblDpGfNjJHNS5UX7rhhLr1FdEycCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd4b8a93955ff9a3a9efb4d980e931a93ff95962f9ac17b4de469742aef16259","last_reissued_at":"2026-05-18T02:41:51.607247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.607247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.3281","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0a/oYvx5sgGLH53t0K4NUcysoer+8HX0W/9yfY/7qJXRZM0ts5+45M/0OK50jIFcnx+bGuXDuERmnIYYctGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:29:14.860160Z"},"content_sha256":"422f69706d4d6e29940f8cc65f6fff7f24627cff5a8bc0f6ab0bfa93662a7025","schema_version":"1.0","event_id":"sha256:422f69706d4d6e29940f8cc65f6fff7f24627cff5a8bc0f6ab0bfa93662a7025"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:3VFYVE4VL742HKPPWTMYB2JRVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nicholas J. Kuhn","submitted_at":"2008-06-19T20:47:06Z","abstract_excerpt":"We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space.\n  What is most interesting is our method, which replaces his iterated use of the Eilenberg--Moore spectral sequence by a single use of the spectral sequence converging to the mod 2 cohomology of Omega^nX obtained from the Goodwillie tower for the suspension spectrum of Omega^nX. Much of the paper develops basic properties of this spectral sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3281","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":""},"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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BU58eYECJkKQuWZ4n6WgHt/VPyASG8rV5pH6rWGaq9QXO8Dp0xvKV8vpGTWOV/VacJ5+KpXTblXdgvVAl8VTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:29:14.860851Z"},"content_sha256":"15bf1571d37112e910ef8cfe8138a448f5fc68d3bb38fc5389d7e0d7d925e513","schema_version":"1.0","event_id":"sha256:15bf1571d37112e910ef8cfe8138a448f5fc68d3bb38fc5389d7e0d7d925e513"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VFYVE4VL742HKPPWTMYB2JRVE/bundle.json","state_url":"https://pith.science/pith/3VFYVE4VL742HKPPWTMYB2JRVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VFYVE4VL742HKPPWTMYB2JRVE/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":"2026-05-31T15:29:14Z","links":{"resolver":"https://pith.science/pith/3VFYVE4VL742HKPPWTMYB2JRVE","bundle":"https://pith.science/pith/3VFYVE4VL742HKPPWTMYB2JRVE/bundle.json","state":"https://pith.science/pith/3VFYVE4VL742HKPPWTMYB2JRVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VFYVE4VL742HKPPWTMYB2JRVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:3VFYVE4VL742HKPPWTMYB2JRVE","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":"5828fd5eafbdc1b98f43c79e855bcadeecf6c2ed708e5d6a1a36fb01e14e4f7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-06-19T20:47:06Z","title_canon_sha256":"b80bf9ac461a707740824b39bbdc05f80e2f820d75a163d51b92f0a5d7fcf082"},"schema_version":"1.0","source":{"id":"0806.3281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3281","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3281v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3281","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VFYVE4VL742","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3VFYVE4VL742HKPP","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3VFYVE4V","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:15bf1571d37112e910ef8cfe8138a448f5fc68d3bb38fc5389d7e0d7d925e513","target":"graph","created_at":"2026-05-18T02:41:51Z","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"},"paper":{"abstract_excerpt":"We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space.\n  What is most interesting is our method, which replaces his iterated use of the Eilenberg--Moore spectral sequence by a single use of the spectral sequence converging to the mod 2 cohomology of Omega^nX obtained from the Goodwillie tower for the suspension spectrum of Omega^nX. Much of the paper develops basic properties of this spectral sequence.","authors_text":"Nicholas J. Kuhn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-06-19T20:47:06Z","title":"Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3281","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":"sha256:422f69706d4d6e29940f8cc65f6fff7f24627cff5a8bc0f6ab0bfa93662a7025","target":"record","created_at":"2026-05-18T02:41:51Z","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":"5828fd5eafbdc1b98f43c79e855bcadeecf6c2ed708e5d6a1a36fb01e14e4f7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-06-19T20:47:06Z","title_canon_sha256":"b80bf9ac461a707740824b39bbdc05f80e2f820d75a163d51b92f0a5d7fcf082"},"schema_version":"1.0","source":{"id":"0806.3281","kind":"arxiv","version":1}},"canonical_sha256":"dd4b8a93955ff9a3a9efb4d980e931a93ff95962f9ac17b4de469742aef16259","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd4b8a93955ff9a3a9efb4d980e931a93ff95962f9ac17b4de469742aef16259","first_computed_at":"2026-05-18T02:41:51.607247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.607247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"seS3Sd90Mdr5/Ux9CAGhoSimsXHHDYw5EsV3REuuROPG2vAbkTGc3i0NUblDpGfNjJHNS5UX7rhhLr1FdEycCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.607785Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.3281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:422f69706d4d6e29940f8cc65f6fff7f24627cff5a8bc0f6ab0bfa93662a7025","sha256:15bf1571d37112e910ef8cfe8138a448f5fc68d3bb38fc5389d7e0d7d925e513"],"state_sha256":"7731fffe9d5fcd3a18e2cc06e229aa0e94c299b2a4a7a3a758d93b866685af26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF0I4YRxnrRY1S1Niu9rXTNTMAbdKE+BH9GbYjfVcf5pJOuktnky/AyWax7TCFTx9T+TM5qQc1IJ7ID7hGMHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:29:14.864593Z","bundle_sha256":"9749663b3e9519fb175dca50de2c9b94582304764b5d863801a79a9da6335daf"}}