{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:SAZYRSSDLYHCROKSAP6RLFIUPQ","short_pith_number":"pith:SAZYRSSD","canonical_record":{"source":{"id":"cond-mat/9904218","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1999-04-15T19:09:51Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"97188297837c2d3e2741b05db7f31504fb44b369f09db0e82ee9b5009ce6ceec","abstract_canon_sha256":"9f9b291fddb044bc7a39771336cc27e05c14e019ef67d10c9887ee3c3a4dbbea"},"schema_version":"1.0"},"canonical_sha256":"903388ca435e0e28b95203fd1595147c0c3534bced486fba0e866d6137633c04","source":{"kind":"arxiv","id":"cond-mat/9904218","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9904218","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9904218v2","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9904218","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"SAZYRSSDLYHC","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_16","alias_value":"SAZYRSSDLYHCROKS","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_8","alias_value":"SAZYRSSD","created_at":"2026-07-04T16:12:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:SAZYRSSDLYHCROKSAP6RLFIUPQ","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9904218","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1999-04-15T19:09:51Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"97188297837c2d3e2741b05db7f31504fb44b369f09db0e82ee9b5009ce6ceec","abstract_canon_sha256":"9f9b291fddb044bc7a39771336cc27e05c14e019ef67d10c9887ee3c3a4dbbea"},"schema_version":"1.0"},"canonical_sha256":"903388ca435e0e28b95203fd1595147c0c3534bced486fba0e866d6137633c04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:12:35.905302Z","signature_b64":"EhVeDD3tP5Trk/y2kejiYX4f/0vkrb4eX449ziRAytBAWDLAo+gq7aDxyv1i0xc+MVDA82OttxwZjFzVlKVbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"903388ca435e0e28b95203fd1595147c0c3534bced486fba0e866d6137633c04","last_reissued_at":"2026-07-04T16:12:35.904917Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:12:35.904917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9904218","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8bA1x3nO+HMR/XDvv0Vzg0F82dVyGT41+8rkO/boWmnU9qnS//C8aH2H1TQ5DkdRpc86BxYrPIo2pUiXOW+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:02:34.279852Z"},"content_sha256":"5b59259a1cfca7d34074dfe1a575ceb51f870557b86b783f21d146b269c8bf5e","schema_version":"1.0","event_id":"sha256:5b59259a1cfca7d34074dfe1a575ceb51f870557b86b783f21d146b269c8bf5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:SAZYRSSDLYHCROKSAP6RLFIUPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Anders W. Sandvik","submitted_at":"1999-04-15T19:09:51Z","abstract_excerpt":"A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge chains (d=+/-n) coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1)-chain Hamiltonian is solved self-consistently for $n$ up to 4. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9904218","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/9904218/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JLagUWgh4SwcclUp0nLDyL0rBgRXimqIe8TzdV9oUjNJYdlOMs95HoKT8C2eNCbFP+YjT/iPmiDPHkx9tGuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:02:34.280398Z"},"content_sha256":"5eb0153a3963e65b6e7ece0e83d0aa89d3cf29ef1a7c655d54f49aa74dc109a7","schema_version":"1.0","event_id":"sha256:5eb0153a3963e65b6e7ece0e83d0aa89d3cf29ef1a7c655d54f49aa74dc109a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/bundle.json","state_url":"https://pith.science/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/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":"2026-08-08T01:02:34Z","links":{"resolver":"https://pith.science/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ","bundle":"https://pith.science/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/bundle.json","state":"https://pith.science/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAZYRSSDLYHCROKSAP6RLFIUPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:SAZYRSSDLYHCROKSAP6RLFIUPQ","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":"9f9b291fddb044bc7a39771336cc27e05c14e019ef67d10c9887ee3c3a4dbbea","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1999-04-15T19:09:51Z","title_canon_sha256":"97188297837c2d3e2741b05db7f31504fb44b369f09db0e82ee9b5009ce6ceec"},"schema_version":"1.0","source":{"id":"cond-mat/9904218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9904218","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9904218v2","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9904218","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"SAZYRSSDLYHC","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_16","alias_value":"SAZYRSSDLYHCROKS","created_at":"2026-07-04T16:12:35Z"},{"alias_kind":"pith_short_8","alias_value":"SAZYRSSD","created_at":"2026-07-04T16:12:35Z"}],"graph_snapshots":[{"event_id":"sha256:5eb0153a3963e65b6e7ece0e83d0aa89d3cf29ef1a7c655d54f49aa74dc109a7","target":"graph","created_at":"2026-07-04T16:12:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/9904218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge chains (d=+/-n) coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1)-chain Hamiltonian is solved self-consistently for $n$ up to 4. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings al","authors_text":"Anders W. Sandvik","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.str-el","submitted_at":"1999-04-15T19:09:51Z","title":"Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9904218","kind":"arxiv","version":2},"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":"sha256:5b59259a1cfca7d34074dfe1a575ceb51f870557b86b783f21d146b269c8bf5e","target":"record","created_at":"2026-07-04T16:12:35Z","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":"9f9b291fddb044bc7a39771336cc27e05c14e019ef67d10c9887ee3c3a4dbbea","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.str-el","submitted_at":"1999-04-15T19:09:51Z","title_canon_sha256":"97188297837c2d3e2741b05db7f31504fb44b369f09db0e82ee9b5009ce6ceec"},"schema_version":"1.0","source":{"id":"cond-mat/9904218","kind":"arxiv","version":2}},"canonical_sha256":"903388ca435e0e28b95203fd1595147c0c3534bced486fba0e866d6137633c04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"903388ca435e0e28b95203fd1595147c0c3534bced486fba0e866d6137633c04","first_computed_at":"2026-07-04T16:12:35.904917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:12:35.904917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EhVeDD3tP5Trk/y2kejiYX4f/0vkrb4eX449ziRAytBAWDLAo+gq7aDxyv1i0xc+MVDA82OttxwZjFzVlKVbBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:12:35.905302Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9904218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b59259a1cfca7d34074dfe1a575ceb51f870557b86b783f21d146b269c8bf5e","sha256:5eb0153a3963e65b6e7ece0e83d0aa89d3cf29ef1a7c655d54f49aa74dc109a7"],"state_sha256":"bd8de8b67c2f7da7c0b13c7697bc01466b3303a2eeb97ab3d1b7ebc354c8a97d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQ6j8iwTGB4bdlQ8ULU3Laop+sW9YGN7YJX2HGovXKk+2LBj6QBHOMhAYoM0RCxE1w19wAij1SBo5Yw0qVA1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T01:02:34.285871Z","bundle_sha256":"fbe7a57b177b5dde295a1683c882e12766e5b5f8428f497c7fd02dc299938938"}}