{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:Q4FP4LQV6UAWSMPGIGGMITV72H","short_pith_number":"pith:Q4FP4LQV","canonical_record":{"source":{"id":"cond-mat/9406003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1994-06-01T11:55:00Z","cross_cats_sorted":[],"title_canon_sha256":"b3c1e25a82a43fcfe114495c725ddb9b7895d70209e8a563cc90902a6ece0c03","abstract_canon_sha256":"54c0d20522d50356e5fd9a0cc4abb78a9c644e96d8a14ffae6df6f4a1e9e0cb5"},"schema_version":"1.0"},"canonical_sha256":"870afe2e15f5016931e6418cc44ebfd1d59ef2411b564f6addd496baa82c675a","source":{"kind":"arxiv","id":"cond-mat/9406003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9406003","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9406003v1","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9406003","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q4FP4LQV6UAW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"Q4FP4LQV6UAWSMPG","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"Q4FP4LQV","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:Q4FP4LQV6UAWSMPGIGGMITV72H","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9406003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1994-06-01T11:55:00Z","cross_cats_sorted":[],"title_canon_sha256":"b3c1e25a82a43fcfe114495c725ddb9b7895d70209e8a563cc90902a6ece0c03","abstract_canon_sha256":"54c0d20522d50356e5fd9a0cc4abb78a9c644e96d8a14ffae6df6f4a1e9e0cb5"},"schema_version":"1.0"},"canonical_sha256":"870afe2e15f5016931e6418cc44ebfd1d59ef2411b564f6addd496baa82c675a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:02.603727Z","signature_b64":"8pr1oiHV10reMurbpaYtQgnq4iu2TG3PZB8r6M2uPBYnnfzBaMxufYEtJFjfE98nNAxo+FsV19VfeeAWS3uqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"870afe2e15f5016931e6418cc44ebfd1d59ef2411b564f6addd496baa82c675a","last_reissued_at":"2026-05-18T03:07:02.603219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:02.603219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9406003","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":"2026-05-18T03:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Em9RoAlT0DD2+a6OgYgjT9FV8M2tF5GLZW/MFEB9aErY5qtrChrstmCMUDuuuoC/DZ83SBGpjU/YkK+X8l32CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:25:10.916078Z"},"content_sha256":"277e03c66cc6c266854b03265bd9e9514fcb76f4a0f2c83766db6da4710d2211","schema_version":"1.0","event_id":"sha256:277e03c66cc6c266854b03265bd9e9514fcb76f4a0f2c83766db6da4710d2211"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:Q4FP4LQV6UAWSMPGIGGMITV72H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperscaling for polymer rings","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Bertrand Duplantier","submitted_at":"1994-06-01T11:55:00Z","abstract_excerpt":"The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a $ d $-dimensional lattice obeys hyperscaling. The combination $ p_N \\left\\langle R^2 \\right\\rangle^{ d/2}_N\\mu^{ -N}, $ (where $ p_N $ is the number of configurations of an oriented and rooted $ N $-step ring, $ \\left\\langle R^2 \\right\\rangle_ N $ a typical average size squared, and $ \\mu $ the SAW effective connectivity constant of the lattice) is equal for $ N \\longrightarrow \\infty $ to a lattice-dependent constant times a universal amplitude $ A(d). $ The latter amplitude is calculated directly from the minimal c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9406003","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":"2026-05-18T03:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32WLLGAXpr/v6jjJ4eZCkJxF3KMdIHqgRxOsqJwnTLQSV7qq0NqJB6IzARBSsSQHxk+d/YAj0U3NmeLIU/s7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:25:10.916594Z"},"content_sha256":"ca15176017c46adbb3fa8080d455b661a138e5b6717e2068d45ea97e5bb1cfbd","schema_version":"1.0","event_id":"sha256:ca15176017c46adbb3fa8080d455b661a138e5b6717e2068d45ea97e5bb1cfbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/bundle.json","state_url":"https://pith.science/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/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":"2026-05-27T22:25:10Z","links":{"resolver":"https://pith.science/pith/Q4FP4LQV6UAWSMPGIGGMITV72H","bundle":"https://pith.science/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/bundle.json","state":"https://pith.science/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4FP4LQV6UAWSMPGIGGMITV72H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:Q4FP4LQV6UAWSMPGIGGMITV72H","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":"54c0d20522d50356e5fd9a0cc4abb78a9c644e96d8a14ffae6df6f4a1e9e0cb5","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1994-06-01T11:55:00Z","title_canon_sha256":"b3c1e25a82a43fcfe114495c725ddb9b7895d70209e8a563cc90902a6ece0c03"},"schema_version":"1.0","source":{"id":"cond-mat/9406003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9406003","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9406003v1","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9406003","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q4FP4LQV6UAW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"Q4FP4LQV6UAWSMPG","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"Q4FP4LQV","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:ca15176017c46adbb3fa8080d455b661a138e5b6717e2068d45ea97e5bb1cfbd","target":"graph","created_at":"2026-05-18T03:07:02Z","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 statistics of a long closed self-avoiding walk (SAW) or polymer ring on a $ d $-dimensional lattice obeys hyperscaling. The combination $ p_N \\left\\langle R^2 \\right\\rangle^{ d/2}_N\\mu^{ -N}, $ (where $ p_N $ is the number of configurations of an oriented and rooted $ N $-step ring, $ \\left\\langle R^2 \\right\\rangle_ N $ a typical average size squared, and $ \\mu $ the SAW effective connectivity constant of the lattice) is equal for $ N \\longrightarrow \\infty $ to a lattice-dependent constant times a universal amplitude $ A(d). $ The latter amplitude is calculated directly from the minimal c","authors_text":"Bertrand Duplantier","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"1994-06-01T11:55:00Z","title":"Hyperscaling for polymer rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9406003","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":"sha256:277e03c66cc6c266854b03265bd9e9514fcb76f4a0f2c83766db6da4710d2211","target":"record","created_at":"2026-05-18T03:07:02Z","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":"54c0d20522d50356e5fd9a0cc4abb78a9c644e96d8a14ffae6df6f4a1e9e0cb5","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1994-06-01T11:55:00Z","title_canon_sha256":"b3c1e25a82a43fcfe114495c725ddb9b7895d70209e8a563cc90902a6ece0c03"},"schema_version":"1.0","source":{"id":"cond-mat/9406003","kind":"arxiv","version":1}},"canonical_sha256":"870afe2e15f5016931e6418cc44ebfd1d59ef2411b564f6addd496baa82c675a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"870afe2e15f5016931e6418cc44ebfd1d59ef2411b564f6addd496baa82c675a","first_computed_at":"2026-05-18T03:07:02.603219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:02.603219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8pr1oiHV10reMurbpaYtQgnq4iu2TG3PZB8r6M2uPBYnnfzBaMxufYEtJFjfE98nNAxo+FsV19VfeeAWS3uqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:02.603727Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9406003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:277e03c66cc6c266854b03265bd9e9514fcb76f4a0f2c83766db6da4710d2211","sha256:ca15176017c46adbb3fa8080d455b661a138e5b6717e2068d45ea97e5bb1cfbd"],"state_sha256":"d618e631d4e1bc1a0f6b023526c595b3995fa9833b967c5314130812ee4e17c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VKsojgDBRh8IRGvaMBXAheZWiGUQtBN8DhGLQGMdkpElBeMLuDsPxpc29j26GfC2fPfee32C7K/ttfqcAyrfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:25:10.920092Z","bundle_sha256":"fefa8d971380d5543067b4373b4a9994a5ebb5b72d75f0413c083a601db5b866"}}