{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QJ7W3M65SAHCTECXWT63NCOG5R","short_pith_number":"pith:QJ7W3M65","canonical_record":{"source":{"id":"1406.3286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-12T16:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"b68164fb73f259d23848ec9710304b87677e958f3a81dad0df3479beeebd7413","abstract_canon_sha256":"716b89800325495545dce6bc7f721dda2b23df5aef2d4d9e8e747993130203cb"},"schema_version":"1.0"},"canonical_sha256":"827f6db3dd900e299057b4fdb689c6ec7df16ef7155f6e44923e2582d288d623","source":{"kind":"arxiv","id":"1406.3286","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3286","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3286v2","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3286","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"QJ7W3M65SAHC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJ7W3M65SAHCTECX","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJ7W3M65","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QJ7W3M65SAHCTECXWT63NCOG5R","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-12T16:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"b68164fb73f259d23848ec9710304b87677e958f3a81dad0df3479beeebd7413","abstract_canon_sha256":"716b89800325495545dce6bc7f721dda2b23df5aef2d4d9e8e747993130203cb"},"schema_version":"1.0"},"canonical_sha256":"827f6db3dd900e299057b4fdb689c6ec7df16ef7155f6e44923e2582d288d623","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:10.394540Z","signature_b64":"ePHSK5q4V3uhamXdsbd9eFJfUtBe0r+xixD2SKuA39UiApSIrzBZUT/wzRjKkXy1YfSPMx3mXLmgY7DRY8y/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"827f6db3dd900e299057b4fdb689c6ec7df16ef7155f6e44923e2582d288d623","last_reissued_at":"2026-05-18T02:20:10.393891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:10.393891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3286","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imyz9+wP2L/bcXhmgVx9wxmkptVuXaYwkOY01JLQkVy9p5+GJ3+g2GKGxQMLXsLgPQqpdwqVF3ERSvXsnBgaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:22:12.795533Z"},"content_sha256":"fa980d374800f66b06bcc4d2d5016343374262a2b019b7d290a2e7ddf48bc043","schema_version":"1.0","event_id":"sha256:fa980d374800f66b06bcc4d2d5016343374262a2b019b7d290a2e7ddf48bc043"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QJ7W3M65SAHCTECXWT63NCOG5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on Hopkins' chromatic splitting conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jack Morava","submitted_at":"2014-06-12T16:57:01Z","abstract_excerpt":"Ravenel proved the remarkable fact that the $K$-theoretic localization $L_K S^0$ of the sphere spectrum has $\\mathbb{Q}/\\mathbb{Z}$ as homotopy group in dimension -2. Mike Hopkins' chromatic splitting conjecture implies more generally that there are $3^{n-1}$ copies of $(\\mathbb{Q}/\\mathbb{Z})_p$ in the homotopy groups of the $E(n)$-localization of $S^0$; but where these copies occur can be confusing. We try here to simplify this book-keeping."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3286","kind":"arxiv","version":2},"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":"2026-05-18T02:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4nSNxRxduxZdTdFr8ehlZIegkz1r+lj8k/cwT4xrNPkml3OiFeFWLNKxg6gYQJ2lNsvbCFhiMsDqgDChwElCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:22:12.795875Z"},"content_sha256":"2eff7ceb9119ea795226c727030b46acd52a9112d0413a0c5895197d2c2a51f0","schema_version":"1.0","event_id":"sha256:2eff7ceb9119ea795226c727030b46acd52a9112d0413a0c5895197d2c2a51f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJ7W3M65SAHCTECXWT63NCOG5R/bundle.json","state_url":"https://pith.science/pith/QJ7W3M65SAHCTECXWT63NCOG5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJ7W3M65SAHCTECXWT63NCOG5R/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":"2026-05-28T10:22:12Z","links":{"resolver":"https://pith.science/pith/QJ7W3M65SAHCTECXWT63NCOG5R","bundle":"https://pith.science/pith/QJ7W3M65SAHCTECXWT63NCOG5R/bundle.json","state":"https://pith.science/pith/QJ7W3M65SAHCTECXWT63NCOG5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJ7W3M65SAHCTECXWT63NCOG5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QJ7W3M65SAHCTECXWT63NCOG5R","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":"716b89800325495545dce6bc7f721dda2b23df5aef2d4d9e8e747993130203cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-12T16:57:01Z","title_canon_sha256":"b68164fb73f259d23848ec9710304b87677e958f3a81dad0df3479beeebd7413"},"schema_version":"1.0","source":{"id":"1406.3286","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3286","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3286v2","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3286","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"QJ7W3M65SAHC","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QJ7W3M65SAHCTECX","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QJ7W3M65","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:2eff7ceb9119ea795226c727030b46acd52a9112d0413a0c5895197d2c2a51f0","target":"graph","created_at":"2026-05-18T02:20:10Z","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":"Ravenel proved the remarkable fact that the $K$-theoretic localization $L_K S^0$ of the sphere spectrum has $\\mathbb{Q}/\\mathbb{Z}$ as homotopy group in dimension -2. Mike Hopkins' chromatic splitting conjecture implies more generally that there are $3^{n-1}$ copies of $(\\mathbb{Q}/\\mathbb{Z})_p$ in the homotopy groups of the $E(n)$-localization of $S^0$; but where these copies occur can be confusing. We try here to simplify this book-keeping.","authors_text":"Jack Morava","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-12T16:57:01Z","title":"A remark on Hopkins' chromatic splitting conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3286","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:fa980d374800f66b06bcc4d2d5016343374262a2b019b7d290a2e7ddf48bc043","target":"record","created_at":"2026-05-18T02:20:10Z","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":"716b89800325495545dce6bc7f721dda2b23df5aef2d4d9e8e747993130203cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-12T16:57:01Z","title_canon_sha256":"b68164fb73f259d23848ec9710304b87677e958f3a81dad0df3479beeebd7413"},"schema_version":"1.0","source":{"id":"1406.3286","kind":"arxiv","version":2}},"canonical_sha256":"827f6db3dd900e299057b4fdb689c6ec7df16ef7155f6e44923e2582d288d623","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"827f6db3dd900e299057b4fdb689c6ec7df16ef7155f6e44923e2582d288d623","first_computed_at":"2026-05-18T02:20:10.393891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:10.393891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ePHSK5q4V3uhamXdsbd9eFJfUtBe0r+xixD2SKuA39UiApSIrzBZUT/wzRjKkXy1YfSPMx3mXLmgY7DRY8y/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:10.394540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3286","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa980d374800f66b06bcc4d2d5016343374262a2b019b7d290a2e7ddf48bc043","sha256:2eff7ceb9119ea795226c727030b46acd52a9112d0413a0c5895197d2c2a51f0"],"state_sha256":"baee165f1dd141fc64807fe540804f697eef5acb9df9b6a8ef37019d1a51939f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owkY3qB04xf4/ajXV8SEvVAfAEHx6PPGWMzBA3blQNnmDUZ2RjQjgnwneHMVin6LoQq7yhxPyeFt/5NfTfFgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:22:12.797687Z","bundle_sha256":"7bc98b457bbee7decc350576e5b3c0d0c0f077e6f1ccaf7195010019bd32e1d7"}}