{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GORBAEDRM5DGCJ2YPP3PT3YL74","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":"88453ff9d13808cd779689152b567fa464069cb431cf151232fb9f42a576cdc0","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-25T14:53:17Z","title_canon_sha256":"3b0eed99ce608ed5fe552fa585b7b664fc120cfc4a7561bbc494543b2a0f20b6"},"schema_version":"1.0","source":{"id":"2506.20507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.20507","created_at":"2026-07-05T12:05:18Z"},{"alias_kind":"arxiv_version","alias_value":"2506.20507v2","created_at":"2026-07-05T12:05:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20507","created_at":"2026-07-05T12:05:18Z"},{"alias_kind":"pith_short_12","alias_value":"GORBAEDRM5DG","created_at":"2026-07-05T12:05:18Z"},{"alias_kind":"pith_short_16","alias_value":"GORBAEDRM5DGCJ2Y","created_at":"2026-07-05T12:05:18Z"},{"alias_kind":"pith_short_8","alias_value":"GORBAEDR","created_at":"2026-07-05T12:05:18Z"}],"graph_snapshots":[{"event_id":"sha256:f87e827d3b92e87903aea45a687567f283130563962cdb2faa6111d3a9e25e5f","target":"graph","created_at":"2026-07-05T12:05:18Z","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/2506.20507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discover a host of infinite periodic families in the 2-primary stable homotopy groups of spheres. We also confirm the existence of many families predicted by Hopkins--Mahowald. These families appear in nineteen different congruence classes of degrees modulo 192, seven of them consist of simple 4-torsion elements, and another four of simple 8-torsion. They all vanish in the homotopy groups of the spectrum TMF of topological modular forms, but we show that they are detected in the fixed-points of TMF with respect to an Atkin--Lehner involution. As a consequence, we confirm the existence of ex","authors_text":"Christian Carrick, Jack Morgan Davies","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-25T14:53:17Z","title":"On periodic families in the stable stems of height two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20507","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:c6a547e00dce09d09ce93eefa17213f0fda696f1c38de3e1b9c3bb8fc555d36a","target":"record","created_at":"2026-07-05T12:05:18Z","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":"88453ff9d13808cd779689152b567fa464069cb431cf151232fb9f42a576cdc0","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-25T14:53:17Z","title_canon_sha256":"3b0eed99ce608ed5fe552fa585b7b664fc120cfc4a7561bbc494543b2a0f20b6"},"schema_version":"1.0","source":{"id":"2506.20507","kind":"arxiv","version":2}},"canonical_sha256":"33a210107167466127587bf6f9ef0bff16597887384f64b38713712b0d2c2e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33a210107167466127587bf6f9ef0bff16597887384f64b38713712b0d2c2e75","first_computed_at":"2026-07-05T12:05:18.058896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:18.058896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CssoRaJRTIyV+ijxAaOaNxSZTe7Ew47cHUURXrg7+ZLzIksQNaxVtU2sp8E/QQlhxjEEQeO3x8/rNraNrn+ECw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:18.059411Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.20507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6a547e00dce09d09ce93eefa17213f0fda696f1c38de3e1b9c3bb8fc555d36a","sha256:f87e827d3b92e87903aea45a687567f283130563962cdb2faa6111d3a9e25e5f"],"state_sha256":"682c698e17710a91632bceab3f923af03f1d63a470f00a6b9a138b5948c037cf"}