{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:EFB5C37MNKL432YTGN46UNT7UP","short_pith_number":"pith:EFB5C37M","canonical_record":{"source":{"id":"2305.02308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-05-03T17:54:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"31f8be8ba4fe029125014658e89067812128444dfb2d2ae52db4d5c000e4cbc3","abstract_canon_sha256":"a2c6b2d58261c55cd94ed6353a1ae0347f3225db13b56653d40e8fd8a381d0d5"},"schema_version":"1.0"},"canonical_sha256":"2143d16fec6a97cdeb133379ea367fa3f710b4f836810c4f7bf0c7554b8332be","source":{"kind":"arxiv","id":"2305.02308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.02308","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"2305.02308v1","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.02308","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"EFB5C37MNKL4","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_16","alias_value":"EFB5C37MNKL432YT","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_8","alias_value":"EFB5C37M","created_at":"2026-07-05T06:06:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:EFB5C37MNKL432YTGN46UNT7UP","target":"record","payload":{"canonical_record":{"source":{"id":"2305.02308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-05-03T17:54:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"31f8be8ba4fe029125014658e89067812128444dfb2d2ae52db4d5c000e4cbc3","abstract_canon_sha256":"a2c6b2d58261c55cd94ed6353a1ae0347f3225db13b56653d40e8fd8a381d0d5"},"schema_version":"1.0"},"canonical_sha256":"2143d16fec6a97cdeb133379ea367fa3f710b4f836810c4f7bf0c7554b8332be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:06:49.855269Z","signature_b64":"Soihm1ILvVS48rgcIAmE4gK3VM5PG+cH0t7HUJrEK/nOvMc9ue/3LoehE/AahOTSkgjZStrKYwgENoaEzBdvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2143d16fec6a97cdeb133379ea367fa3f710b4f836810c4f7bf0c7554b8332be","last_reissued_at":"2026-07-05T06:06:49.854872Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:06:49.854872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.02308","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ny9vl08ON1U8EElYNnyknaLzOlyMu+V+zYkE80LTpXlLh9xpmfrfJXvTaRpRy3/K18AtQkE+PeDsYb9+KAkkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:47:42.382294Z"},"content_sha256":"3de805d072af9be55db69e35786d1254d5fc81d3cedf8744f18d45f9fea3229c","schema_version":"1.0","event_id":"sha256:3de805d072af9be55db69e35786d1254d5fc81d3cedf8744f18d45f9fea3229c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:EFB5C37MNKL432YTGN46UNT7UP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Descent in tensor triangular geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Beren Sanders, Drew Heard, Luca Pol, Natalia Castellana, Niko Naumann, Tobias Barthel","submitted_at":"2023-05-03T17:54:53Z","abstract_excerpt":"We investigate to what extent we can descend the classification of localizing, smashing and thick ideals in a presentably symmetric monoidal stable $\\infty$-category $\\mathscr{C}$ along a descendable commutative algebra $A$. We establish equalizer diagrams relating the lattices of localizing and smashing ideals of $\\mathscr{C}$ to those of $\\mathrm{Mod}_{A}(\\mathscr{C})$ and $\\mathrm{Mod}_{A\\otimes A}(\\mathscr{C})$. If $A$ is compact, we obtain a similar equalizer for the lattices of thick ideals which, via Stone duality, yields a coequalizer diagram of Balmer spectra in the category of spectr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.02308","kind":"arxiv","version":1},"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/2305.02308/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":"2026-07-05T06:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYrymwTS7VIOTxW97rIp8/YNGu3tgZ4vRiGBMJ143vL1NrIUKsPDWgWWjPqNlx4Z9Mv/TaWy39pzWaILgeS5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:47:42.382791Z"},"content_sha256":"bc45f84f132338021c6552b3a27e8633bde079aaebb4f699a7dec099654fcc8c","schema_version":"1.0","event_id":"sha256:bc45f84f132338021c6552b3a27e8633bde079aaebb4f699a7dec099654fcc8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFB5C37MNKL432YTGN46UNT7UP/bundle.json","state_url":"https://pith.science/pith/EFB5C37MNKL432YTGN46UNT7UP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFB5C37MNKL432YTGN46UNT7UP/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":"2026-08-09T09:47:42Z","links":{"resolver":"https://pith.science/pith/EFB5C37MNKL432YTGN46UNT7UP","bundle":"https://pith.science/pith/EFB5C37MNKL432YTGN46UNT7UP/bundle.json","state":"https://pith.science/pith/EFB5C37MNKL432YTGN46UNT7UP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFB5C37MNKL432YTGN46UNT7UP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EFB5C37MNKL432YTGN46UNT7UP","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":"a2c6b2d58261c55cd94ed6353a1ae0347f3225db13b56653d40e8fd8a381d0d5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-05-03T17:54:53Z","title_canon_sha256":"31f8be8ba4fe029125014658e89067812128444dfb2d2ae52db4d5c000e4cbc3"},"schema_version":"1.0","source":{"id":"2305.02308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.02308","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"2305.02308v1","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.02308","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"EFB5C37MNKL4","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_16","alias_value":"EFB5C37MNKL432YT","created_at":"2026-07-05T06:06:49Z"},{"alias_kind":"pith_short_8","alias_value":"EFB5C37M","created_at":"2026-07-05T06:06:49Z"}],"graph_snapshots":[{"event_id":"sha256:bc45f84f132338021c6552b3a27e8633bde079aaebb4f699a7dec099654fcc8c","target":"graph","created_at":"2026-07-05T06:06:49Z","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/2305.02308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate to what extent we can descend the classification of localizing, smashing and thick ideals in a presentably symmetric monoidal stable $\\infty$-category $\\mathscr{C}$ along a descendable commutative algebra $A$. We establish equalizer diagrams relating the lattices of localizing and smashing ideals of $\\mathscr{C}$ to those of $\\mathrm{Mod}_{A}(\\mathscr{C})$ and $\\mathrm{Mod}_{A\\otimes A}(\\mathscr{C})$. If $A$ is compact, we obtain a similar equalizer for the lattices of thick ideals which, via Stone duality, yields a coequalizer diagram of Balmer spectra in the category of spectr","authors_text":"Beren Sanders, Drew Heard, Luca Pol, Natalia Castellana, Niko Naumann, Tobias Barthel","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-05-03T17:54:53Z","title":"Descent in tensor triangular geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.02308","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":"sha256:3de805d072af9be55db69e35786d1254d5fc81d3cedf8744f18d45f9fea3229c","target":"record","created_at":"2026-07-05T06:06:49Z","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":"a2c6b2d58261c55cd94ed6353a1ae0347f3225db13b56653d40e8fd8a381d0d5","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-05-03T17:54:53Z","title_canon_sha256":"31f8be8ba4fe029125014658e89067812128444dfb2d2ae52db4d5c000e4cbc3"},"schema_version":"1.0","source":{"id":"2305.02308","kind":"arxiv","version":1}},"canonical_sha256":"2143d16fec6a97cdeb133379ea367fa3f710b4f836810c4f7bf0c7554b8332be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2143d16fec6a97cdeb133379ea367fa3f710b4f836810c4f7bf0c7554b8332be","first_computed_at":"2026-07-05T06:06:49.854872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:06:49.854872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Soihm1ILvVS48rgcIAmE4gK3VM5PG+cH0t7HUJrEK/nOvMc9ue/3LoehE/AahOTSkgjZStrKYwgENoaEzBdvAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:06:49.855269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.02308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3de805d072af9be55db69e35786d1254d5fc81d3cedf8744f18d45f9fea3229c","sha256:bc45f84f132338021c6552b3a27e8633bde079aaebb4f699a7dec099654fcc8c"],"state_sha256":"4726e762768a6c1c1591920b767ee2b6d804459a0e9ffa4f502b229acea9241d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DoSnwBtjP7lVaaQAlOILU6B4aHsCDEICGgYjPu5hMQzRLCPWJwkLiYyM2uT7+2w/LDmf1uHVVzfzvI4Lv1+SCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:47:42.386251Z","bundle_sha256":"45a6116bc2be128e5e8469ef0708d0d4dd3836744b5ac2b6082d0b04c479b571"}}