{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HANK5YHAT2PVJKT5BBKYX5FR4A","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":"60832e058ac57458b9da9ae3333af6b56070ad7400a39307c0ac43042672fedd","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-08-02T23:58:38Z","title_canon_sha256":"26fd9237eeb3d51eb8bfbbec74ab07dcf98663f55a0980afcf87626a29398145"},"schema_version":"1.0","source":{"id":"2508.01524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.01524","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"2508.01524v2","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.01524","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"HANK5YHAT2PV","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_16","alias_value":"HANK5YHAT2PVJKT5","created_at":"2026-05-29T02:05:35Z"},{"alias_kind":"pith_short_8","alias_value":"HANK5YHA","created_at":"2026-05-29T02:05:35Z"}],"graph_snapshots":[{"event_id":"sha256:c5d7d57652bb584ccb0fca84260349de338c99ac9abd854120d1fed9762b0ba0","target":"graph","created_at":"2026-05-29T02:05:35Z","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/2508.01524/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a very special $\\Gamma$-space $X$, repeated application of Segal's delooping functor produces the constituent spaces of the associated connective $\\Omega$-spectrum. In particular, by applying this construction to \\textit{discrete} very special $\\Gamma$-spaces (a.k.a.~Abelian groups), one recovers Eilenberg-MacLane spectra. The delooping functor is entirely formal, however, and can be applied to arbitrary $\\Gamma$-spaces without any conditions. Work of Connes and Consani suggests that the ``field with one element'' can be fruitfully realized as a (discrete) $\\Gamma$-space (which localizes","authors_text":"Jonathan Beardsley","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-08-02T23:58:38Z","title":"The Eilenberg-MacLane Spectrum of \\mathbb{F}_1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01524","kind":"arxiv","version":2},"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":"sha256:0182a138b48e77362611df18f379c3a7b6d18b805f9b0b0cf79292661ccba24a","target":"record","created_at":"2026-05-29T02:05:35Z","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":"60832e058ac57458b9da9ae3333af6b56070ad7400a39307c0ac43042672fedd","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-08-02T23:58:38Z","title_canon_sha256":"26fd9237eeb3d51eb8bfbbec74ab07dcf98663f55a0980afcf87626a29398145"},"schema_version":"1.0","source":{"id":"2508.01524","kind":"arxiv","version":2}},"canonical_sha256":"381aaee0e09e9f54aa7d08558bf4b1e02db79751c7da35b01e3e9a5ac9a6640e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"381aaee0e09e9f54aa7d08558bf4b1e02db79751c7da35b01e3e9a5ac9a6640e","first_computed_at":"2026-05-29T02:05:35.652593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:35.652593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xl/CuxYjm+tIi+IPL0yveAl+GRG/oylbvg9lMkui85r6Rss3//RXIyRVOuKI7jO9gPcZn5RZHxZR9r+arQSUAQ==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:35.653150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.01524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0182a138b48e77362611df18f379c3a7b6d18b805f9b0b0cf79292661ccba24a","sha256:c5d7d57652bb584ccb0fca84260349de338c99ac9abd854120d1fed9762b0ba0"],"state_sha256":"e189a5fcd1bf05c760ff46c7a2d8b62ecdaa273ffca84af87a36e3afe61d06b2"}