{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VSKQZGLTYQZS3ERR2VBABSJQ5P","short_pith_number":"pith:VSKQZGLT","canonical_record":{"source":{"id":"2607.10865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-12T18:00:08Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"title_canon_sha256":"0abcf9fed64c8b8085da4af58855d726ca260fddb78df901e59d973be4d7402a","abstract_canon_sha256":"8ce314254c536a38b936017bfb195377e53035c6692cb58f7d107099d4ab1530"},"schema_version":"1.0"},"canonical_sha256":"ac950c9973c4332d9231d54200c930ebe0c8e6dda9e06524694ef8208e617342","source":{"kind":"arxiv","id":"2607.10865","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10865","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10865v1","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10865","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"VSKQZGLTYQZS","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_16","alias_value":"VSKQZGLTYQZS3ERR","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_8","alias_value":"VSKQZGLT","created_at":"2026-07-14T01:21:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VSKQZGLTYQZS3ERR2VBABSJQ5P","target":"record","payload":{"canonical_record":{"source":{"id":"2607.10865","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-12T18:00:08Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"title_canon_sha256":"0abcf9fed64c8b8085da4af58855d726ca260fddb78df901e59d973be4d7402a","abstract_canon_sha256":"8ce314254c536a38b936017bfb195377e53035c6692cb58f7d107099d4ab1530"},"schema_version":"1.0"},"canonical_sha256":"ac950c9973c4332d9231d54200c930ebe0c8e6dda9e06524694ef8208e617342","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:44.242067Z","signature_b64":"gSWnExXdoUyTomp3S8XKBmN6ctZiH91kIAjeqCaqyL0jXTC3PFPoEp/RVlBYrzi/8U0ToUEvzqwDI6xZlpDOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac950c9973c4332d9231d54200c930ebe0c8e6dda9e06524694ef8208e617342","last_reissued_at":"2026-07-14T01:21:44.241204Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:44.241204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.10865","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":"2026-07-14T01:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NeGFhTMkW8JC8OZ0IWWppFN0TFNdSnAR92NG84bsJyAZigsVjXpyl+3pQ/PPIprPkHzW6AuirYLp0XM4Q8V4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:04:14.300658Z"},"content_sha256":"f4bb1ea9aa6394e905e17d6493191c878a279affc69acea5b5a1160e1163480c","schema_version":"1.0","event_id":"sha256:f4bb1ea9aa6394e905e17d6493191c878a279affc69acea5b5a1160e1163480c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VSKQZGLTYQZS3ERR2VBABSJQ5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensional and Spin Interpolation for the O$(n)$ Model: From Exact Anchors to RG-Improved Critical Exponents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.chem-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kumar Ghosh","submitted_at":"2026-07-12T18:00:08Z","abstract_excerpt":"We develop a two-axis interpolation framework for the O$(n)$ universality family, treating the spatial dimension $D$ and the spin-component number $n$ as independent continuous parameters connecting exact limiting solutions. On the spatial axis, anchoring between the Onsager solution at $D=2$ and mean-field theory at $D\\to\\infty$ yields a closed-form prediction for the 3D Ising critical coupling that agrees well with Monte Carlo benchmarks $K_c = 0.2204$ (benchmark: $0.22165$) with no adjustable parameters. Wilson--Fisher-constrained polynomial interpolation gives $\\nu=2/3$, $\\beta=31/96$, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10865","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10865/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":"2026-07-14T01:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6scvJFOWuENFHMnD+NOYBcAz2BaO3PWIT8gduuZj/JvFE29EFB/hw0AF8aNTEzbw74qDeq91HISn+Q49KEPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:04:14.301171Z"},"content_sha256":"3f8e3c49a8342de13fb5ed1f9a3a088b39b61780b09bfbe3a8444ce9c293e3ce","schema_version":"1.0","event_id":"sha256:3f8e3c49a8342de13fb5ed1f9a3a088b39b61780b09bfbe3a8444ce9c293e3ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/bundle.json","state_url":"https://pith.science/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/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":"2026-08-04T12:04:14Z","links":{"resolver":"https://pith.science/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P","bundle":"https://pith.science/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/bundle.json","state":"https://pith.science/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSKQZGLTYQZS3ERR2VBABSJQ5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VSKQZGLTYQZS3ERR2VBABSJQ5P","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":"8ce314254c536a38b936017bfb195377e53035c6692cb58f7d107099d4ab1530","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-12T18:00:08Z","title_canon_sha256":"0abcf9fed64c8b8085da4af58855d726ca260fddb78df901e59d973be4d7402a"},"schema_version":"1.0","source":{"id":"2607.10865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10865","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10865v1","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10865","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"VSKQZGLTYQZS","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_16","alias_value":"VSKQZGLTYQZS3ERR","created_at":"2026-07-14T01:21:44Z"},{"alias_kind":"pith_short_8","alias_value":"VSKQZGLT","created_at":"2026-07-14T01:21:44Z"}],"graph_snapshots":[{"event_id":"sha256:3f8e3c49a8342de13fb5ed1f9a3a088b39b61780b09bfbe3a8444ce9c293e3ce","target":"graph","created_at":"2026-07-14T01:21:44Z","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/2607.10865/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a two-axis interpolation framework for the O$(n)$ universality family, treating the spatial dimension $D$ and the spin-component number $n$ as independent continuous parameters connecting exact limiting solutions. On the spatial axis, anchoring between the Onsager solution at $D=2$ and mean-field theory at $D\\to\\infty$ yields a closed-form prediction for the 3D Ising critical coupling that agrees well with Monte Carlo benchmarks $K_c = 0.2204$ (benchmark: $0.22165$) with no adjustable parameters. Wilson--Fisher-constrained polynomial interpolation gives $\\nu=2/3$, $\\beta=31/96$, and","authors_text":"Kumar Ghosh","cross_cats":["math-ph","math.MP","physics.chem-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-12T18:00:08Z","title":"Dimensional and Spin Interpolation for the O$(n)$ Model: From Exact Anchors to RG-Improved Critical Exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10865","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:f4bb1ea9aa6394e905e17d6493191c878a279affc69acea5b5a1160e1163480c","target":"record","created_at":"2026-07-14T01:21:44Z","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":"8ce314254c536a38b936017bfb195377e53035c6692cb58f7d107099d4ab1530","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-12T18:00:08Z","title_canon_sha256":"0abcf9fed64c8b8085da4af58855d726ca260fddb78df901e59d973be4d7402a"},"schema_version":"1.0","source":{"id":"2607.10865","kind":"arxiv","version":1}},"canonical_sha256":"ac950c9973c4332d9231d54200c930ebe0c8e6dda9e06524694ef8208e617342","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac950c9973c4332d9231d54200c930ebe0c8e6dda9e06524694ef8208e617342","first_computed_at":"2026-07-14T01:21:44.241204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:21:44.241204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSWnExXdoUyTomp3S8XKBmN6ctZiH91kIAjeqCaqyL0jXTC3PFPoEp/RVlBYrzi/8U0ToUEvzqwDI6xZlpDOCg==","signature_status":"signed_v1","signed_at":"2026-07-14T01:21:44.242067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4bb1ea9aa6394e905e17d6493191c878a279affc69acea5b5a1160e1163480c","sha256:3f8e3c49a8342de13fb5ed1f9a3a088b39b61780b09bfbe3a8444ce9c293e3ce"],"state_sha256":"87ad3c043422d57457ba94aa71fe9991a6cacd22d1dddc67c7fa087465a94aa3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DHDenjMe0O59h1S9DjehTLUGEYDzsIHp6KQ8Pdt4tiur+ZXb9NzbyuyylAWrLoj0wee+VauAHF9Z9Uj8ykFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:04:14.304849Z","bundle_sha256":"fa7f0263e29aa3f83e032b8c1b85f06f8bf96b4d6f0ecb3ff04099a96e8a9b6a"}}