{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TQKHD2GUQVG7DTHOEZE52Y63RB","short_pith_number":"pith:TQKHD2GU","canonical_record":{"source":{"id":"1709.04828","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-14T15:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"6615ca54ee9b9a16dfea6058cc4ff4974e64ae15f25b71030752c847e4433f06","abstract_canon_sha256":"a2bf029e05645d982dc760e69e08dbe12c01eeddc30e52b5004a9d45a6f2fd93"},"schema_version":"1.0"},"canonical_sha256":"9c1471e8d4854df1ccee2649dd63db88647eca500197a11f8c7c4953ff93f203","source":{"kind":"arxiv","id":"1709.04828","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04828","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04828v3","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04828","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_12","alias_value":"TQKHD2GUQVG7","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_16","alias_value":"TQKHD2GUQVG7DTHO","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_8","alias_value":"TQKHD2GU","created_at":"2026-07-05T06:31:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TQKHD2GUQVG7DTHOEZE52Y63RB","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04828","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-14T15:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"6615ca54ee9b9a16dfea6058cc4ff4974e64ae15f25b71030752c847e4433f06","abstract_canon_sha256":"a2bf029e05645d982dc760e69e08dbe12c01eeddc30e52b5004a9d45a6f2fd93"},"schema_version":"1.0"},"canonical_sha256":"9c1471e8d4854df1ccee2649dd63db88647eca500197a11f8c7c4953ff93f203","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:31:50.322474Z","signature_b64":"ue8I8a55ZlLm/LCk84KGi9zG/OJIy8p83EswpKrKgax1BI3yAE68e9QAuDANo6v81iBR0A/f9shHGVhXXkGTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c1471e8d4854df1ccee2649dd63db88647eca500197a11f8c7c4953ff93f203","last_reissued_at":"2026-07-05T06:31:50.322061Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:31:50.322061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04828","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:31:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/9uOl3jiYGszCEXvO1N4JUSfxVoSdknl9oP8oEUeSqZQPuef5ilXczXGFnhU4M0rjFxKjKQIHoqNpQQ87b+rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:31:34.481139Z"},"content_sha256":"e003675fdb639038f8388b4f1729bab3e30c4c11cc0dea1398586170fe9c310f","schema_version":"1.0","event_id":"sha256:e003675fdb639038f8388b4f1729bab3e30c4c11cc0dea1398586170fe9c310f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TQKHD2GUQVG7DTHOEZE52Y63RB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Balmer spectrum of the equivariant homotopy category of a finite abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Justin Noel, Markus Hausmann, Nathaniel Stapleton, Niko Naumann, Thomas Nikolaus, Tobias Barthel","submitted_at":"2017-09-14T15:00:09Z","abstract_excerpt":"For a finite abelian group $A$, we determine the Balmer spectrum of $\\mathrm{Sp}_A^{\\omega}$, the compact objects in genuine $A$-spectra. This generalizes the case $A=\\mathbb{Z}/p\\mathbb{Z}$ due to Balmer and Sanders \\cite{Balmer-Sanders}, by establishing (a corrected version of) their log$_p$-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions \\cite{kuhn}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04828","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1709.04828/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:31:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8skjoGHkfuuImOGJWJ3lIvRZIJ0/RvSWntOZl0L3DVrtBkiL9NyeWuRU5kmg2cyZnTupXHKHamYdH12SzsidBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:31:34.481530Z"},"content_sha256":"aa5b94b6a8034c4fd9dbc986c96ccca565f409f99876fa46359d01d215fcb1a9","schema_version":"1.0","event_id":"sha256:aa5b94b6a8034c4fd9dbc986c96ccca565f409f99876fa46359d01d215fcb1a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/bundle.json","state_url":"https://pith.science/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/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":"2026-07-06T19:31:34Z","links":{"resolver":"https://pith.science/pith/TQKHD2GUQVG7DTHOEZE52Y63RB","bundle":"https://pith.science/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/bundle.json","state":"https://pith.science/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQKHD2GUQVG7DTHOEZE52Y63RB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TQKHD2GUQVG7DTHOEZE52Y63RB","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":"a2bf029e05645d982dc760e69e08dbe12c01eeddc30e52b5004a9d45a6f2fd93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-14T15:00:09Z","title_canon_sha256":"6615ca54ee9b9a16dfea6058cc4ff4974e64ae15f25b71030752c847e4433f06"},"schema_version":"1.0","source":{"id":"1709.04828","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04828","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04828v3","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04828","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_12","alias_value":"TQKHD2GUQVG7","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_16","alias_value":"TQKHD2GUQVG7DTHO","created_at":"2026-07-05T06:31:50Z"},{"alias_kind":"pith_short_8","alias_value":"TQKHD2GU","created_at":"2026-07-05T06:31:50Z"}],"graph_snapshots":[{"event_id":"sha256:aa5b94b6a8034c4fd9dbc986c96ccca565f409f99876fa46359d01d215fcb1a9","target":"graph","created_at":"2026-07-05T06:31:50Z","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/1709.04828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a finite abelian group $A$, we determine the Balmer spectrum of $\\mathrm{Sp}_A^{\\omega}$, the compact objects in genuine $A$-spectra. This generalizes the case $A=\\mathbb{Z}/p\\mathbb{Z}$ due to Balmer and Sanders \\cite{Balmer-Sanders}, by establishing (a corrected version of) their log$_p$-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions \\cite{kuhn}.","authors_text":"Justin Noel, Markus Hausmann, Nathaniel Stapleton, Niko Naumann, Thomas Nikolaus, Tobias Barthel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-14T15:00:09Z","title":"The Balmer spectrum of the equivariant homotopy category of a finite abelian group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04828","kind":"arxiv","version":3},"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:e003675fdb639038f8388b4f1729bab3e30c4c11cc0dea1398586170fe9c310f","target":"record","created_at":"2026-07-05T06:31:50Z","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":"a2bf029e05645d982dc760e69e08dbe12c01eeddc30e52b5004a9d45a6f2fd93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-09-14T15:00:09Z","title_canon_sha256":"6615ca54ee9b9a16dfea6058cc4ff4974e64ae15f25b71030752c847e4433f06"},"schema_version":"1.0","source":{"id":"1709.04828","kind":"arxiv","version":3}},"canonical_sha256":"9c1471e8d4854df1ccee2649dd63db88647eca500197a11f8c7c4953ff93f203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c1471e8d4854df1ccee2649dd63db88647eca500197a11f8c7c4953ff93f203","first_computed_at":"2026-07-05T06:31:50.322061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:31:50.322061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ue8I8a55ZlLm/LCk84KGi9zG/OJIy8p83EswpKrKgax1BI3yAE68e9QAuDANo6v81iBR0A/f9shHGVhXXkGTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:31:50.322474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04828","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e003675fdb639038f8388b4f1729bab3e30c4c11cc0dea1398586170fe9c310f","sha256:aa5b94b6a8034c4fd9dbc986c96ccca565f409f99876fa46359d01d215fcb1a9"],"state_sha256":"00264baee6570cd0b9096b0f82228b145d4f49fab501d7cb126b5fc3d4996be5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nhj52UXbxPpw0Q+DyaZP250qNjBFgUNaCEKfEhGAqCeTchjJ4813oMKXwJjErfrmdZA2IJM8ki/5a8+gRXh2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:31:34.483492Z","bundle_sha256":"36c88c56988ddad6937f1d18e3ca28cc87780ae0287f79dab5b5945efc9d0047"}}