{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RUTFNSMMQ6WZ4UTXJ3EW4HK5S4","short_pith_number":"pith:RUTFNSMM","canonical_record":{"source":{"id":"1108.3509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-17T15:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"e1dc7394de82b649984e5d53c5702f16ca711081f4a09cadb17f9e090152fa74","abstract_canon_sha256":"ea703f660c84cf0c208be808beebf461211e59eec5b6215122327c109e40e36a"},"schema_version":"1.0"},"canonical_sha256":"8d2656c98c87ad9e52774ec96e1d5d973a27d95b70a86861907113c7ac35f909","source":{"kind":"arxiv","id":"1108.3509","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3509","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3509v3","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3509","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"RUTFNSMMQ6WZ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUTFNSMMQ6WZ4UTX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUTFNSMM","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RUTFNSMMQ6WZ4UTXJ3EW4HK5S4","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-17T15:41:34Z","cross_cats_sorted":[],"title_canon_sha256":"e1dc7394de82b649984e5d53c5702f16ca711081f4a09cadb17f9e090152fa74","abstract_canon_sha256":"ea703f660c84cf0c208be808beebf461211e59eec5b6215122327c109e40e36a"},"schema_version":"1.0"},"canonical_sha256":"8d2656c98c87ad9e52774ec96e1d5d973a27d95b70a86861907113c7ac35f909","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:21.767682Z","signature_b64":"r1S2Zoiq+fdmY03/cIsJiVHA+SI1hrdxTI4DvTXh2Re8F499ZwIGoDr+1bHB0D8melKO/NNUkKNsRH1MLQh4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d2656c98c87ad9e52774ec96e1d5d973a27d95b70a86861907113c7ac35f909","last_reissued_at":"2026-05-18T02:16:21.766956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:21.766956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3509","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":"2026-05-18T02:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ljq7xdwu/wTD3wSmO0Dv2qgO1oKIgIQ1v8sF0+4ilbo1yFICmTvgJs+uCMXfom3ndKFJJFl/7rmTrlBJmz6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:00:59.426666Z"},"content_sha256":"a2263c9637d9f10d2512d0324c7475871358309baebc2774f427f167dd831381","schema_version":"1.0","event_id":"sha256:a2263c9637d9f10d2512d0324c7475871358309baebc2774f427f167dd831381"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RUTFNSMMQ6WZ4UTXJ3EW4HK5S4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive model structures for abstract symmetric spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Sergey Gorchinskiy, Vladimir Guletskii","submitted_at":"2011-08-17T15:41:34Z","abstract_excerpt":"We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3509","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":""},"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":"2026-05-18T02:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dm7Ayclh4mnNu1g+qFEdE2lUXxCL4Yn98XW9XgFiXZYSbDxp5EntA5Y5rNtXl0n6kqbdL68mBzGZf7qwcd0uCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:00:59.427043Z"},"content_sha256":"e3421319abc040c84c83e231484ecbf6d16c05fc82eb2fa1f334be91f34fd48b","schema_version":"1.0","event_id":"sha256:e3421319abc040c84c83e231484ecbf6d16c05fc82eb2fa1f334be91f34fd48b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/bundle.json","state_url":"https://pith.science/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/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":"2026-05-31T03:00:59Z","links":{"resolver":"https://pith.science/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4","bundle":"https://pith.science/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/bundle.json","state":"https://pith.science/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUTFNSMMQ6WZ4UTXJ3EW4HK5S4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RUTFNSMMQ6WZ4UTXJ3EW4HK5S4","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":"ea703f660c84cf0c208be808beebf461211e59eec5b6215122327c109e40e36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-17T15:41:34Z","title_canon_sha256":"e1dc7394de82b649984e5d53c5702f16ca711081f4a09cadb17f9e090152fa74"},"schema_version":"1.0","source":{"id":"1108.3509","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3509","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3509v3","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3509","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"RUTFNSMMQ6WZ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUTFNSMMQ6WZ4UTX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUTFNSMM","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:e3421319abc040c84c83e231484ecbf6d16c05fc82eb2fa1f334be91f34fd48b","target":"graph","created_at":"2026-05-18T02:16:21Z","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":"We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version.","authors_text":"Sergey Gorchinskiy, Vladimir Guletskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-17T15:41:34Z","title":"Positive model structures for abstract symmetric spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3509","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:a2263c9637d9f10d2512d0324c7475871358309baebc2774f427f167dd831381","target":"record","created_at":"2026-05-18T02:16:21Z","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":"ea703f660c84cf0c208be808beebf461211e59eec5b6215122327c109e40e36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-17T15:41:34Z","title_canon_sha256":"e1dc7394de82b649984e5d53c5702f16ca711081f4a09cadb17f9e090152fa74"},"schema_version":"1.0","source":{"id":"1108.3509","kind":"arxiv","version":3}},"canonical_sha256":"8d2656c98c87ad9e52774ec96e1d5d973a27d95b70a86861907113c7ac35f909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d2656c98c87ad9e52774ec96e1d5d973a27d95b70a86861907113c7ac35f909","first_computed_at":"2026-05-18T02:16:21.766956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:21.766956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r1S2Zoiq+fdmY03/cIsJiVHA+SI1hrdxTI4DvTXh2Re8F499ZwIGoDr+1bHB0D8melKO/NNUkKNsRH1MLQh4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:21.767682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3509","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2263c9637d9f10d2512d0324c7475871358309baebc2774f427f167dd831381","sha256:e3421319abc040c84c83e231484ecbf6d16c05fc82eb2fa1f334be91f34fd48b"],"state_sha256":"e2ff433901a3c4844c92c7a8793c30bf758628422f0750d8f13f4f8e10a6fcea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SbE+Fc/dBf6zJZWWa78GalYLo0WoLPcv4XtMTL7G//+VJ7t8Z6QbB4SuzSSsWEdmXR4d1iZbjkaJrSyW1+YBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:00:59.428968Z","bundle_sha256":"896d06fe856b9f46d3ddc7fcb3408ab42eb8c2188b40c1266902be8d7ecde025"}}