{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:M3UIAFV4OB53LYPTC5MCY7JLU2","short_pith_number":"pith:M3UIAFV4","canonical_record":{"source":{"id":"1010.2338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-12T09:54:27Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"f123a2eae8b9a78d8aa0050c8edc91ae5c1d4ad9d7fd526f2eec544b0ab50aac","abstract_canon_sha256":"5a288d6c695a7c1e712c8ed4659f61cd6ff6007247a235e808b315487782f39c"},"schema_version":"1.0"},"canonical_sha256":"66e88016bc707bb5e1f317582c7d2ba693ab4855afb022bf9ae6fff0c5e12988","source":{"kind":"arxiv","id":"1010.2338","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2338","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2338v1","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2338","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"pith_short_12","alias_value":"M3UIAFV4OB53","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"M3UIAFV4OB53LYPT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"M3UIAFV4","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:M3UIAFV4OB53LYPTC5MCY7JLU2","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-12T09:54:27Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"f123a2eae8b9a78d8aa0050c8edc91ae5c1d4ad9d7fd526f2eec544b0ab50aac","abstract_canon_sha256":"5a288d6c695a7c1e712c8ed4659f61cd6ff6007247a235e808b315487782f39c"},"schema_version":"1.0"},"canonical_sha256":"66e88016bc707bb5e1f317582c7d2ba693ab4855afb022bf9ae6fff0c5e12988","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:06.126545Z","signature_b64":"aisE5i+zcccYt1Lk0WJhU+Ru6ymrGZjYY87hlkEsB2Bk4flslFJgTv8Lp2UD5QJzubwMGkmu8pmWPZL9EJz+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66e88016bc707bb5e1f317582c7d2ba693ab4855afb022bf9ae6fff0c5e12988","last_reissued_at":"2026-05-18T02:05:06.125796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:06.125796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2338","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":"2026-05-18T02:05:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65Px4jJuCkACGyivn+IUVJ3tnwaEcxnOtS+viQhL8CJR67ravDFU8rllGyCOzx5iQJGmB7FNZsUS1rP4Nbj1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:20:43.582533Z"},"content_sha256":"79bf33e5a985abb2fad0cb7640f131e463afe446a82800374241fcefbce2ba0a","schema_version":"1.0","event_id":"sha256:79bf33e5a985abb2fad0cb7640f131e463afe446a82800374241fcefbce2ba0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:M3UIAFV4OB53LYPTC5MCY7JLU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Aernout C.D. van Enter, Ellis de Groote","submitted_at":"2010-10-12T09:54:27Z","abstract_excerpt":"We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2338","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":"2026-05-18T02:05:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/CWfunmzXR9xHzZsP31RqtxzducWWi60V7BzmlgF3INw0wX4bJdJWOpFiYkNkhM2mQXfyFPgtkQQoBMrV45KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:20:43.582883Z"},"content_sha256":"acfb3db19e639d42d99bbc3e7c2e19dd928051083a105c7490831f9d3ac47d72","schema_version":"1.0","event_id":"sha256:acfb3db19e639d42d99bbc3e7c2e19dd928051083a105c7490831f9d3ac47d72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/bundle.json","state_url":"https://pith.science/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/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":"2026-06-03T14:20:43Z","links":{"resolver":"https://pith.science/pith/M3UIAFV4OB53LYPTC5MCY7JLU2","bundle":"https://pith.science/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/bundle.json","state":"https://pith.science/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M3UIAFV4OB53LYPTC5MCY7JLU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:M3UIAFV4OB53LYPTC5MCY7JLU2","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":"5a288d6c695a7c1e712c8ed4659f61cd6ff6007247a235e808b315487782f39c","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-12T09:54:27Z","title_canon_sha256":"f123a2eae8b9a78d8aa0050c8edc91ae5c1d4ad9d7fd526f2eec544b0ab50aac"},"schema_version":"1.0","source":{"id":"1010.2338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2338","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2338v1","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2338","created_at":"2026-05-18T02:05:06Z"},{"alias_kind":"pith_short_12","alias_value":"M3UIAFV4OB53","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"M3UIAFV4OB53LYPT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"M3UIAFV4","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:acfb3db19e639d42d99bbc3e7c2e19dd928051083a105c7490831f9d3ac47d72","target":"graph","created_at":"2026-05-18T02:05:06Z","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 compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models.","authors_text":"Aernout C.D. van Enter, Ellis de Groote","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-12T09:54:27Z","title":"An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2338","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":"sha256:79bf33e5a985abb2fad0cb7640f131e463afe446a82800374241fcefbce2ba0a","target":"record","created_at":"2026-05-18T02:05:06Z","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":"5a288d6c695a7c1e712c8ed4659f61cd6ff6007247a235e808b315487782f39c","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-12T09:54:27Z","title_canon_sha256":"f123a2eae8b9a78d8aa0050c8edc91ae5c1d4ad9d7fd526f2eec544b0ab50aac"},"schema_version":"1.0","source":{"id":"1010.2338","kind":"arxiv","version":1}},"canonical_sha256":"66e88016bc707bb5e1f317582c7d2ba693ab4855afb022bf9ae6fff0c5e12988","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66e88016bc707bb5e1f317582c7d2ba693ab4855afb022bf9ae6fff0c5e12988","first_computed_at":"2026-05-18T02:05:06.125796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:06.125796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aisE5i+zcccYt1Lk0WJhU+Ru6ymrGZjYY87hlkEsB2Bk4flslFJgTv8Lp2UD5QJzubwMGkmu8pmWPZL9EJz+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:06.126545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79bf33e5a985abb2fad0cb7640f131e463afe446a82800374241fcefbce2ba0a","sha256:acfb3db19e639d42d99bbc3e7c2e19dd928051083a105c7490831f9d3ac47d72"],"state_sha256":"51dfee9a30a6bad848d8f37fe2a91f4a0a3c7b0cd9799ce3c6890d149c23e38b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kicvHHB/uqcmZeD98m9CC8C2jt47toFbdoNTRb16fkDIEjTw6lEFtTnuO1dx5VLmBSqif2vvz1AbiuW8NCSgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:20:43.584844Z","bundle_sha256":"29f010e3156aa54611be6e506459b40beea62857e9dc2107fb0862544440335c"}}