{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WZP2CAKRHALFZIILU4I3BXIW2Q","short_pith_number":"pith:WZP2CAKR","canonical_record":{"source":{"id":"1604.08190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-04-27T19:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"4ddaac4dc4a07df93a7ba5da2a052d1836186a56ef9248b5cdad1641e12ee194","abstract_canon_sha256":"29fd8c4f17b3e4692b887c7ec5ac2ffac809fdbd0c6e1aa1e58fd65ab0a2ed21"},"schema_version":"1.0"},"canonical_sha256":"b65fa1015138165ca10ba711b0dd16d43d6032f6fecc2c0ed0074da6a2715791","source":{"kind":"arxiv","id":"1604.08190","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08190","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08190v2","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08190","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"WZP2CAKRHALF","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZP2CAKRHALFZIIL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZP2CAKR","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WZP2CAKRHALFZIILU4I3BXIW2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1604.08190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-04-27T19:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"4ddaac4dc4a07df93a7ba5da2a052d1836186a56ef9248b5cdad1641e12ee194","abstract_canon_sha256":"29fd8c4f17b3e4692b887c7ec5ac2ffac809fdbd0c6e1aa1e58fd65ab0a2ed21"},"schema_version":"1.0"},"canonical_sha256":"b65fa1015138165ca10ba711b0dd16d43d6032f6fecc2c0ed0074da6a2715791","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:52.258407Z","signature_b64":"aR4jpeq2vI07G/+NAFF63Aij6MD1pVcJVB4xlC2jdIJd76I+A+iQGh4dPFrHoRdqv39YlGYBd9b3NQZc5m2IBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b65fa1015138165ca10ba711b0dd16d43d6032f6fecc2c0ed0074da6a2715791","last_reissued_at":"2026-05-18T00:50:52.257928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:52.257928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.08190","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":"2026-05-18T00:50:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0xBsQOpimXgSYjCMAHBviMtJvKZuT6Wx/1hk1UlCQSxW6vTZSYgnkA6Xq31xsRubDl1NyCKKW1qPFVlO3m8kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:07.006663Z"},"content_sha256":"5cb46fd8cda082f40749f3859c46913701d04bee9203cd9ea703e49583859961","schema_version":"1.0","event_id":"sha256:5cb46fd8cda082f40749f3859c46913701d04bee9203cd9ea703e49583859961"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WZP2CAKRHALFZIILU4I3BXIW2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The replica symmetric solution for Orthogonally Constrained Heisenberg Model on Bethe lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Francesco Concetti","submitted_at":"2016-04-27T19:27:22Z","abstract_excerpt":"In this paper, we study the thermodynamic properties of a system of $D$-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction $J(\\mathbf{S}_i\\cdot \\mathbf{S}_k)^2$. We can consider this model as a continuum version of anti-ferromagnetic $D$-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through the linear stability analysis, we obtain an instability line on the temperature-connectivity plane th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08190","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":""},"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":"2026-05-18T00:50:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdCR1RVKpkESmFawuRmj8e8dV8Tma4kWuJkVFNAfnMTZXMAdAPr4Cs0B/ijKSeKhCKykDiI2z9SLclXX5pmkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:07.007053Z"},"content_sha256":"63eb078f6260946c2627880aa2372e9ad6f00565b4d40b0c0dddd851578f13f3","schema_version":"1.0","event_id":"sha256:63eb078f6260946c2627880aa2372e9ad6f00565b4d40b0c0dddd851578f13f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/bundle.json","state_url":"https://pith.science/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/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":"2026-06-25T20:43:07Z","links":{"resolver":"https://pith.science/pith/WZP2CAKRHALFZIILU4I3BXIW2Q","bundle":"https://pith.science/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/bundle.json","state":"https://pith.science/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZP2CAKRHALFZIILU4I3BXIW2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WZP2CAKRHALFZIILU4I3BXIW2Q","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":"29fd8c4f17b3e4692b887c7ec5ac2ffac809fdbd0c6e1aa1e58fd65ab0a2ed21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-04-27T19:27:22Z","title_canon_sha256":"4ddaac4dc4a07df93a7ba5da2a052d1836186a56ef9248b5cdad1641e12ee194"},"schema_version":"1.0","source":{"id":"1604.08190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08190","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08190v2","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08190","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"WZP2CAKRHALF","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZP2CAKRHALFZIIL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZP2CAKR","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:63eb078f6260946c2627880aa2372e9ad6f00565b4d40b0c0dddd851578f13f3","target":"graph","created_at":"2026-05-18T00:50:52Z","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":"In this paper, we study the thermodynamic properties of a system of $D$-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction $J(\\mathbf{S}_i\\cdot \\mathbf{S}_k)^2$. We can consider this model as a continuum version of anti-ferromagnetic $D$-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through the linear stability analysis, we obtain an instability line on the temperature-connectivity plane th","authors_text":"Francesco Concetti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-04-27T19:27:22Z","title":"The replica symmetric solution for Orthogonally Constrained Heisenberg Model on Bethe lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08190","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":"sha256:5cb46fd8cda082f40749f3859c46913701d04bee9203cd9ea703e49583859961","target":"record","created_at":"2026-05-18T00:50:52Z","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":"29fd8c4f17b3e4692b887c7ec5ac2ffac809fdbd0c6e1aa1e58fd65ab0a2ed21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2016-04-27T19:27:22Z","title_canon_sha256":"4ddaac4dc4a07df93a7ba5da2a052d1836186a56ef9248b5cdad1641e12ee194"},"schema_version":"1.0","source":{"id":"1604.08190","kind":"arxiv","version":2}},"canonical_sha256":"b65fa1015138165ca10ba711b0dd16d43d6032f6fecc2c0ed0074da6a2715791","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b65fa1015138165ca10ba711b0dd16d43d6032f6fecc2c0ed0074da6a2715791","first_computed_at":"2026-05-18T00:50:52.257928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:52.257928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aR4jpeq2vI07G/+NAFF63Aij6MD1pVcJVB4xlC2jdIJd76I+A+iQGh4dPFrHoRdqv39YlGYBd9b3NQZc5m2IBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:52.258407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cb46fd8cda082f40749f3859c46913701d04bee9203cd9ea703e49583859961","sha256:63eb078f6260946c2627880aa2372e9ad6f00565b4d40b0c0dddd851578f13f3"],"state_sha256":"ea9da36d8a0a13a9019196b8d55f0f734c55152427df9c0a59e8c8524f91341d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpE3p6PXTpROmHiwZhbcNqzUAVOYMU+7SW2aCgcoxz2FRf4Ido4Qneix34M1MEEnN5Lrwo0AkYT4SQJ38O0OBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:43:07.009292Z","bundle_sha256":"ae8ed13ae413ec3492d9bcfe2fa9bac1c30440ede686e2703a7e55d592f9972a"}}