{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GWE4TPACGATFMAMUGQAARALMYS","short_pith_number":"pith:GWE4TPAC","canonical_record":{"source":{"id":"1206.0651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"d863d802e6bf3e00e9ee99bc150eba71de39dcc5cef43851ff4fc2a255aab476","abstract_canon_sha256":"d567fc32051a997917d799e474966f843c9421408ac57668530ee4c28a1ac58a"},"schema_version":"1.0"},"canonical_sha256":"3589c9bc023026560194340008816cc495245b58ce87b57de1e0d283dc5b3984","source":{"kind":"arxiv","id":"1206.0651","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0651","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0651v1","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0651","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"GWE4TPACGATF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GWE4TPACGATFMAMU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GWE4TPAC","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GWE4TPACGATFMAMUGQAARALMYS","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"d863d802e6bf3e00e9ee99bc150eba71de39dcc5cef43851ff4fc2a255aab476","abstract_canon_sha256":"d567fc32051a997917d799e474966f843c9421408ac57668530ee4c28a1ac58a"},"schema_version":"1.0"},"canonical_sha256":"3589c9bc023026560194340008816cc495245b58ce87b57de1e0d283dc5b3984","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:17.034636Z","signature_b64":"RY+KiQgdGywvi7O/fHI/U9wDkIWNc0ye7p4pvEL1l3gLurmtuEV0j0kfcxo2Ms0v1dE8fODcYdy0s0Ne1CVCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3589c9bc023026560194340008816cc495245b58ce87b57de1e0d283dc5b3984","last_reissued_at":"2026-05-18T03:54:17.034006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:17.034006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0651","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":"2026-05-18T03:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2rftylxAu167Ts92mje4BLeXkHByqmc2CHq9HHxV5L4WmeBIiD7QqWVkZ9+WeJf2522OmT3vipj6soBGkamBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:19.020885Z"},"content_sha256":"8ae0ed59f9d685e2c3fe0473920b8f85c9ae9729256ac8c9136b374378e702cf","schema_version":"1.0","event_id":"sha256:8ae0ed59f9d685e2c3fe0473920b8f85c9ae9729256ac8c9136b374378e702cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GWE4TPACGATFMAMUGQAARALMYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A type (4) space in (FR)-classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anna Pelczar-Barwacz, Antonis Manoussakis, Spiros A. Argyros","submitted_at":"2012-06-04T15:34:01Z","abstract_excerpt":"We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0651","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":""},"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":"2026-05-18T03:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stvVi/Vtep2Ck7fGv5f4z5Sn0BOEs8oNyqreGBV3FjKJiYFdti1Ctdc+j6jJuV/wIP6tr9qw/ivMpa2i7H9kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:19.021623Z"},"content_sha256":"28ba7b505fea1c3d93abb71c21d70550948e403f40369c777250ecc9e5338568","schema_version":"1.0","event_id":"sha256:28ba7b505fea1c3d93abb71c21d70550948e403f40369c777250ecc9e5338568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWE4TPACGATFMAMUGQAARALMYS/bundle.json","state_url":"https://pith.science/pith/GWE4TPACGATFMAMUGQAARALMYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWE4TPACGATFMAMUGQAARALMYS/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":"2026-06-09T22:46:19Z","links":{"resolver":"https://pith.science/pith/GWE4TPACGATFMAMUGQAARALMYS","bundle":"https://pith.science/pith/GWE4TPACGATFMAMUGQAARALMYS/bundle.json","state":"https://pith.science/pith/GWE4TPACGATFMAMUGQAARALMYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWE4TPACGATFMAMUGQAARALMYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GWE4TPACGATFMAMUGQAARALMYS","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":"d567fc32051a997917d799e474966f843c9421408ac57668530ee4c28a1ac58a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:34:01Z","title_canon_sha256":"d863d802e6bf3e00e9ee99bc150eba71de39dcc5cef43851ff4fc2a255aab476"},"schema_version":"1.0","source":{"id":"1206.0651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0651","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0651v1","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0651","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"GWE4TPACGATF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GWE4TPACGATFMAMU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GWE4TPAC","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:28ba7b505fea1c3d93abb71c21d70550948e403f40369c777250ecc9e5338568","target":"graph","created_at":"2026-05-18T03:54:17Z","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 present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.","authors_text":"Anna Pelczar-Barwacz, Antonis Manoussakis, Spiros A. Argyros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:34:01Z","title":"A type (4) space in (FR)-classification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0651","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":"sha256:8ae0ed59f9d685e2c3fe0473920b8f85c9ae9729256ac8c9136b374378e702cf","target":"record","created_at":"2026-05-18T03:54:17Z","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":"d567fc32051a997917d799e474966f843c9421408ac57668530ee4c28a1ac58a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:34:01Z","title_canon_sha256":"d863d802e6bf3e00e9ee99bc150eba71de39dcc5cef43851ff4fc2a255aab476"},"schema_version":"1.0","source":{"id":"1206.0651","kind":"arxiv","version":1}},"canonical_sha256":"3589c9bc023026560194340008816cc495245b58ce87b57de1e0d283dc5b3984","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3589c9bc023026560194340008816cc495245b58ce87b57de1e0d283dc5b3984","first_computed_at":"2026-05-18T03:54:17.034006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:17.034006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RY+KiQgdGywvi7O/fHI/U9wDkIWNc0ye7p4pvEL1l3gLurmtuEV0j0kfcxo2Ms0v1dE8fODcYdy0s0Ne1CVCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:17.034636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ae0ed59f9d685e2c3fe0473920b8f85c9ae9729256ac8c9136b374378e702cf","sha256:28ba7b505fea1c3d93abb71c21d70550948e403f40369c777250ecc9e5338568"],"state_sha256":"418c01186de65ab951bf68e9aed471f9e31c90c58df917986531c4f30f936b12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EgGyBtFGbUHVo+l14u4a9ID9ke0ZZA3wyU87QAgxhQ9P24EALtmWH/iBaev/oRxJE8HWSOqKGedjW/7cQrSpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:46:19.025428Z","bundle_sha256":"f7e175d7d52975e958bf579b65bada58f5ea824589d2f77b5b2e7dca37e81b0f"}}