{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U3ZTHAPKMF7A3RRYZCIFUOD45Q","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":"ea7f26e45338a29896044d29c361adc14312ac0a5c67fb0c7711b8d631b08311","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2019-03-17T15:56:04Z","title_canon_sha256":"d47ee13aecc5f41f7aa6ee6acec8655678cd056a0434f5eb3368ce4294a1c5cd"},"schema_version":"1.0","source":{"id":"1903.07116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07116","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07116v1","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07116","created_at":"2026-05-17T23:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"U3ZTHAPKMF7A","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U3ZTHAPKMF7A3RRY","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U3ZTHAPK","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:6fecc393e71916f6b759832272750d2c4f416940e7b9fb79fb55d095649c937b","target":"graph","created_at":"2026-05-17T23:51:04Z","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":"Many interesting spectra can be constructed as Thom spectra of easily constructed bundles. Mahowald showed that $\\mathit{bu}$ and $\\mathit{bo}$ cannot be realized as $E_1$ Thom spectra. We use related techniques to show that $\\mathit{tmf}_{(2)}$ also cannot be realized as an $E_1$ Thom spectrum.","authors_text":"Hood Chatham","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2019-03-17T15:56:04Z","title":"Thom Complexes and the Spectrum tmf"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07116","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:b54dbf0c13e2c5660e2562657129b0eabcc5bfe2e84c053823506141cb164905","target":"record","created_at":"2026-05-17T23:51:04Z","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":"ea7f26e45338a29896044d29c361adc14312ac0a5c67fb0c7711b8d631b08311","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2019-03-17T15:56:04Z","title_canon_sha256":"d47ee13aecc5f41f7aa6ee6acec8655678cd056a0434f5eb3368ce4294a1c5cd"},"schema_version":"1.0","source":{"id":"1903.07116","kind":"arxiv","version":1}},"canonical_sha256":"a6f33381ea617e0dc638c8905a387cec170fae291c5fd62509a8866c131ba780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6f33381ea617e0dc638c8905a387cec170fae291c5fd62509a8866c131ba780","first_computed_at":"2026-05-17T23:51:04.175733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:04.175733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2NIevtgEotMRA3No1Ri0yZ05285cKb+2tykeG0A368wRZxiUwiDn3j9OXW+TPejHGuhKIYNI7S+fJ4q2ClGAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:04.176311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b54dbf0c13e2c5660e2562657129b0eabcc5bfe2e84c053823506141cb164905","sha256:6fecc393e71916f6b759832272750d2c4f416940e7b9fb79fb55d095649c937b"],"state_sha256":"4778c815a7630a76599caa621f8d7a6bbfc021a74785ae5ef84dbf858a5c5fb1"}