{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ABACC5GTWPEPW5UF7FX275NQZB","short_pith_number":"pith:ABACC5GT","canonical_record":{"source":{"id":"1306.3809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-17T10:59:50Z","cross_cats_sorted":["math-ph","math.MP","stat.ML"],"title_canon_sha256":"074c06fa03bdf03842f02555b1630056c9452ca443415d7657da13b5e3ac8b93","abstract_canon_sha256":"ce05be954bc3c99d427166d8b832258a63bb1c9c57fb85abd87062ccd7dfb546"},"schema_version":"1.0"},"canonical_sha256":"00402174d3b3c8fb7685f96faff5b0c846454d3e67a141c28b9f008ea93cb6e7","source":{"kind":"arxiv","id":"1306.3809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3809","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3809v1","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3809","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"ABACC5GTWPEP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABACC5GTWPEPW5UF","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABACC5GT","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ABACC5GTWPEPW5UF7FX275NQZB","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-17T10:59:50Z","cross_cats_sorted":["math-ph","math.MP","stat.ML"],"title_canon_sha256":"074c06fa03bdf03842f02555b1630056c9452ca443415d7657da13b5e3ac8b93","abstract_canon_sha256":"ce05be954bc3c99d427166d8b832258a63bb1c9c57fb85abd87062ccd7dfb546"},"schema_version":"1.0"},"canonical_sha256":"00402174d3b3c8fb7685f96faff5b0c846454d3e67a141c28b9f008ea93cb6e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:46.365753Z","signature_b64":"fGXPdxa83N+myvg/Tys9/W6wmK70btDaMhHXJFKsOGumeIN+2fzXC4Quf4r2ggJXU6xugtZ83XjLiGIQ6VyFDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00402174d3b3c8fb7685f96faff5b0c846454d3e67a141c28b9f008ea93cb6e7","last_reissued_at":"2026-05-18T03:20:46.364874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:46.364874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3809","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":"2026-05-18T03:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x59xPAo+8MdMQIqGCMMY2NoOLF56Q315emUFKoTh5vEZbtHixe30+5awWhFY5hZxzyiA4IGDXz81svG7fEkJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T05:06:03.903749Z"},"content_sha256":"d22bf71117ec83792cbf6a442e89fdb7fe38596fcaa81a35ea9572855839e120","schema_version":"1.0","event_id":"sha256:d22bf71117ec83792cbf6a442e89fdb7fe38596fcaa81a35ea9572855839e120"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ABACC5GTWPEPW5UF7FX275NQZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical perceptron as a storage memory with limited errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","stat.ML"],"primary_cat":"math.PR","authors_text":"Mihailo Stojnic","submitted_at":"2013-06-17T10:59:50Z","abstract_excerpt":"It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \\cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. Among the most important ones are of course the storage capacities. The first rigorous confirmations were obtained in \\cite{SchTir02,SchTir03} for the storage capacity of the so-called positive spherical perceptron. These were later reestablished in \\cite{TalBook} and a bit more "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3809","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":"2026-05-18T03:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDGpEs72+umF0UGDw8yzTMXWWwpg0PBJhV4tapb0WybXFYSxmdK4tiiq72xs19JebsjTCG64H2DpIMT1a+1jDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T05:06:03.904176Z"},"content_sha256":"f9f1b0e4026716b824adbaafc923744e53464759aa6c8180bc13f5d1db86f1c6","schema_version":"1.0","event_id":"sha256:f9f1b0e4026716b824adbaafc923744e53464759aa6c8180bc13f5d1db86f1c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABACC5GTWPEPW5UF7FX275NQZB/bundle.json","state_url":"https://pith.science/pith/ABACC5GTWPEPW5UF7FX275NQZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABACC5GTWPEPW5UF7FX275NQZB/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":"2026-05-25T05:06:03Z","links":{"resolver":"https://pith.science/pith/ABACC5GTWPEPW5UF7FX275NQZB","bundle":"https://pith.science/pith/ABACC5GTWPEPW5UF7FX275NQZB/bundle.json","state":"https://pith.science/pith/ABACC5GTWPEPW5UF7FX275NQZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABACC5GTWPEPW5UF7FX275NQZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ABACC5GTWPEPW5UF7FX275NQZB","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":"ce05be954bc3c99d427166d8b832258a63bb1c9c57fb85abd87062ccd7dfb546","cross_cats_sorted":["math-ph","math.MP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-17T10:59:50Z","title_canon_sha256":"074c06fa03bdf03842f02555b1630056c9452ca443415d7657da13b5e3ac8b93"},"schema_version":"1.0","source":{"id":"1306.3809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3809","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3809v1","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3809","created_at":"2026-05-18T03:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"ABACC5GTWPEP","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABACC5GTWPEPW5UF","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABACC5GT","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:f9f1b0e4026716b824adbaafc923744e53464759aa6c8180bc13f5d1db86f1c6","target":"graph","created_at":"2026-05-18T03:20:46Z","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":"It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \\cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. Among the most important ones are of course the storage capacities. The first rigorous confirmations were obtained in \\cite{SchTir02,SchTir03} for the storage capacity of the so-called positive spherical perceptron. These were later reestablished in \\cite{TalBook} and a bit more ","authors_text":"Mihailo Stojnic","cross_cats":["math-ph","math.MP","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-17T10:59:50Z","title":"Spherical perceptron as a storage memory with limited errors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3809","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:d22bf71117ec83792cbf6a442e89fdb7fe38596fcaa81a35ea9572855839e120","target":"record","created_at":"2026-05-18T03:20:46Z","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":"ce05be954bc3c99d427166d8b832258a63bb1c9c57fb85abd87062ccd7dfb546","cross_cats_sorted":["math-ph","math.MP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-17T10:59:50Z","title_canon_sha256":"074c06fa03bdf03842f02555b1630056c9452ca443415d7657da13b5e3ac8b93"},"schema_version":"1.0","source":{"id":"1306.3809","kind":"arxiv","version":1}},"canonical_sha256":"00402174d3b3c8fb7685f96faff5b0c846454d3e67a141c28b9f008ea93cb6e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00402174d3b3c8fb7685f96faff5b0c846454d3e67a141c28b9f008ea93cb6e7","first_computed_at":"2026-05-18T03:20:46.364874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:46.364874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fGXPdxa83N+myvg/Tys9/W6wmK70btDaMhHXJFKsOGumeIN+2fzXC4Quf4r2ggJXU6xugtZ83XjLiGIQ6VyFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:46.365753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d22bf71117ec83792cbf6a442e89fdb7fe38596fcaa81a35ea9572855839e120","sha256:f9f1b0e4026716b824adbaafc923744e53464759aa6c8180bc13f5d1db86f1c6"],"state_sha256":"4d6be780ac907c16c7d0cab1a7a73397a3a6c7a512903b6265fab162afe4d08c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQOj43U9C3GtY7Pix+qlOKWufqyhbXRJ5lHp/SceNzIAdFVpu4VbNz4SoD+mmlQbIjIUH+1FK6gY+a7GK6pyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T05:06:03.907466Z","bundle_sha256":"26f62c5342ec30daf021c18b25448a36d1d9cef70bf7b151d77e4426e57988e8"}}