{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4JDMWKRVWPBV3DZXWSBE5U5R7D","short_pith_number":"pith:4JDMWKRV","canonical_record":{"source":{"id":"1611.02133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-07T15:53:30Z","cross_cats_sorted":[],"title_canon_sha256":"45e054c9a87c1baa3e955d4080995458fa243da585edcc4066998beab8a26e3d","abstract_canon_sha256":"778742d6513038410cf103b270f32b90946b25309d7c960f49b0b7a6c8517b4b"},"schema_version":"1.0"},"canonical_sha256":"e246cb2a35b3c35d8f37b4824ed3b1f8ca4a6af95b6c1a882eb0c021bc944275","source":{"kind":"arxiv","id":"1611.02133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02133","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02133v1","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02133","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"4JDMWKRVWPBV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4JDMWKRVWPBV3DZX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4JDMWKRV","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4JDMWKRVWPBV3DZXWSBE5U5R7D","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-07T15:53:30Z","cross_cats_sorted":[],"title_canon_sha256":"45e054c9a87c1baa3e955d4080995458fa243da585edcc4066998beab8a26e3d","abstract_canon_sha256":"778742d6513038410cf103b270f32b90946b25309d7c960f49b0b7a6c8517b4b"},"schema_version":"1.0"},"canonical_sha256":"e246cb2a35b3c35d8f37b4824ed3b1f8ca4a6af95b6c1a882eb0c021bc944275","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:03.629530Z","signature_b64":"3WnWl259o4ksN45RNPBLPV9yPl8ddhBAL+H5WvrZtdlOANI3y2HnkB+8GV1Si5fiu/wavLvB1nPGwTq2GWsmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e246cb2a35b3c35d8f37b4824ed3b1f8ca4a6af95b6c1a882eb0c021bc944275","last_reissued_at":"2026-05-18T01:00:03.628838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:03.628838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02133","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":"2026-05-18T01:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mowVTlu/qg7SasFTZTpvREucSKn1fqYtwYT8IJumLkxvhDnNJ3x7a2JHgl9Sj0c+3WzzUKJDrgEfQbO9GShxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:33:59.572411Z"},"content_sha256":"e63527ac719daeea712bfaa3e131e8fbc4a6d8f161f0f4b5e035137cfa4224dc","schema_version":"1.0","event_id":"sha256:e63527ac719daeea712bfaa3e131e8fbc4a6d8f161f0f4b5e035137cfa4224dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4JDMWKRVWPBV3DZXWSBE5U5R7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability constants of the weak$^*$ fixed point property for the space $\\ell_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emanuele Casini, Enrico Miglierina, {\\L}ukasz Piasecki, Roxana Popescu","submitted_at":"2016-11-07T15:53:30Z","abstract_excerpt":"The main aim of the paper is to study some quantitative aspects of the stability of the weak$^*$ fixed point property for nonexpansive maps in $\\ell_1$ (shortly, $w^*$-fpp). We focus on two complementary approaches to this topic. First, given a predual $X$ of $\\ell_1$ such that the $\\sigma(\\ell_1,X)$-fpp holds, we precisely establish how far, with respect to the Banach-Mazur distance, we can move from $X$ without losing the $w^*$-fpp. The interesting point to note here is that our estimate depends only on the smallest radius of the ball in $\\ell_1$ containing all $\\sigma(\\ell_1,X)$-cluster poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02133","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":"2026-05-18T01:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1F3cvSHZoWUR4jjNFgasqHBUXbbdyym6p1x9uohPRwDBcUpJ4ZEMUR5M76RcRirOLtefE4n7OLcRxPlfMD2vCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:33:59.572768Z"},"content_sha256":"fcd960a9cf964db47492e682406a067ae609487aa6cabfe7c66b58263c1ca6dc","schema_version":"1.0","event_id":"sha256:fcd960a9cf964db47492e682406a067ae609487aa6cabfe7c66b58263c1ca6dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/bundle.json","state_url":"https://pith.science/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/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":"2026-06-24T10:33:59Z","links":{"resolver":"https://pith.science/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D","bundle":"https://pith.science/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/bundle.json","state":"https://pith.science/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JDMWKRVWPBV3DZXWSBE5U5R7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4JDMWKRVWPBV3DZXWSBE5U5R7D","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":"778742d6513038410cf103b270f32b90946b25309d7c960f49b0b7a6c8517b4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-07T15:53:30Z","title_canon_sha256":"45e054c9a87c1baa3e955d4080995458fa243da585edcc4066998beab8a26e3d"},"schema_version":"1.0","source":{"id":"1611.02133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02133","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02133v1","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02133","created_at":"2026-05-18T01:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"4JDMWKRVWPBV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4JDMWKRVWPBV3DZX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4JDMWKRV","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:fcd960a9cf964db47492e682406a067ae609487aa6cabfe7c66b58263c1ca6dc","target":"graph","created_at":"2026-05-18T01:00:03Z","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":"The main aim of the paper is to study some quantitative aspects of the stability of the weak$^*$ fixed point property for nonexpansive maps in $\\ell_1$ (shortly, $w^*$-fpp). We focus on two complementary approaches to this topic. First, given a predual $X$ of $\\ell_1$ such that the $\\sigma(\\ell_1,X)$-fpp holds, we precisely establish how far, with respect to the Banach-Mazur distance, we can move from $X$ without losing the $w^*$-fpp. The interesting point to note here is that our estimate depends only on the smallest radius of the ball in $\\ell_1$ containing all $\\sigma(\\ell_1,X)$-cluster poi","authors_text":"Emanuele Casini, Enrico Miglierina, {\\L}ukasz Piasecki, Roxana Popescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-07T15:53:30Z","title":"Stability constants of the weak$^*$ fixed point property for the space $\\ell_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02133","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:e63527ac719daeea712bfaa3e131e8fbc4a6d8f161f0f4b5e035137cfa4224dc","target":"record","created_at":"2026-05-18T01:00:03Z","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":"778742d6513038410cf103b270f32b90946b25309d7c960f49b0b7a6c8517b4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-07T15:53:30Z","title_canon_sha256":"45e054c9a87c1baa3e955d4080995458fa243da585edcc4066998beab8a26e3d"},"schema_version":"1.0","source":{"id":"1611.02133","kind":"arxiv","version":1}},"canonical_sha256":"e246cb2a35b3c35d8f37b4824ed3b1f8ca4a6af95b6c1a882eb0c021bc944275","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e246cb2a35b3c35d8f37b4824ed3b1f8ca4a6af95b6c1a882eb0c021bc944275","first_computed_at":"2026-05-18T01:00:03.628838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:03.628838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3WnWl259o4ksN45RNPBLPV9yPl8ddhBAL+H5WvrZtdlOANI3y2HnkB+8GV1Si5fiu/wavLvB1nPGwTq2GWsmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:03.629530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e63527ac719daeea712bfaa3e131e8fbc4a6d8f161f0f4b5e035137cfa4224dc","sha256:fcd960a9cf964db47492e682406a067ae609487aa6cabfe7c66b58263c1ca6dc"],"state_sha256":"31d97e5d22953ef99e4fa569037e55ab85c2d814d9522d34c45602742b07a42a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lB060zRBiYIeieswj7U5Fr9wUihS7g/hpFdkpJ5oHyb84JZAcIVUcBm9wI1XVqkgnLxgJ+c3pUi1XlHBnAZmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:33:59.574741Z","bundle_sha256":"2b00e093283ef84b70880ea67b531be36001692bf3acf9e0861015f3f4a1a1bc"}}