{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DKR6CVW3VBGDOA6D3W3NTS3Q6C","short_pith_number":"pith:DKR6CVW3","canonical_record":{"source":{"id":"2606.13075","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T08:59:34Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"f9ad3c4ebd567f0a113f35d4949999dec8d63ffbabc1363c6c519e245af04ae6","abstract_canon_sha256":"b82c376b22810da1b2911e7ab5f8e985c39f1519a5ee3afb1688b0a5c77f9971"},"schema_version":"1.0"},"canonical_sha256":"1aa3e156dba84c3703c3ddb6d9cb70f0bd095d9350c93934e9481f5de5f0a9d9","source":{"kind":"arxiv","id":"2606.13075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13075","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13075v1","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13075","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"DKR6CVW3VBGD","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_16","alias_value":"DKR6CVW3VBGDOA6D","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_8","alias_value":"DKR6CVW3","created_at":"2026-06-12T01:09:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DKR6CVW3VBGDOA6D3W3NTS3Q6C","target":"record","payload":{"canonical_record":{"source":{"id":"2606.13075","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T08:59:34Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"f9ad3c4ebd567f0a113f35d4949999dec8d63ffbabc1363c6c519e245af04ae6","abstract_canon_sha256":"b82c376b22810da1b2911e7ab5f8e985c39f1519a5ee3afb1688b0a5c77f9971"},"schema_version":"1.0"},"canonical_sha256":"1aa3e156dba84c3703c3ddb6d9cb70f0bd095d9350c93934e9481f5de5f0a9d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:39.303122Z","signature_b64":"eCeOTD8vh7gEplQKaRQfkN1aIZ/JEguEGbQ3ijoIXgzKNYkIM7HaM7zFfjDtuDzzhZDkdDLLQf+GQkTtGgjhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aa3e156dba84c3703c3ddb6d9cb70f0bd095d9350c93934e9481f5de5f0a9d9","last_reissued_at":"2026-06-12T01:09:39.302673Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:39.302673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.13075","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":"2026-06-12T01:09:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5A93Tbkv6bVR9fvPNtAeXAW8klPMYxln7fy71cjxOQI/6WOpPpAEETPXoVZ8dIuMD8wnwjL2xqaP+ekMZmOaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:26:06.248333Z"},"content_sha256":"770150d7c89440d5adcf9620f60d29abdacd5d7d2f77e6bc231ad5e42509bba1","schema_version":"1.0","event_id":"sha256:770150d7c89440d5adcf9620f60d29abdacd5d7d2f77e6bc231ad5e42509bba1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DKR6CVW3VBGDOA6D3W3NTS3Q6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chiral Long-Range Order in three Euclidean Lattice Gross-Neveu Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Leonardo Goller, Simone Fabbri","submitted_at":"2026-06-11T08:59:34Z","abstract_excerpt":"We prove the existence of Long-Range Order in a class of two-dimensional Euclidean lattice Gross-Neveu models with an even number of fermion flavors, covering three standard lattice discretizations, including naive and staggered fermions widely used in numerical studies. By performing a Hubbard-Stratonovich transformation, we map the fermionic systems to bosonic ones and establish Reflection Positivity for the resulting measures. Exploiting this structure, we combine Chessboard Estimates with a Peierls-type contour argument to prove Long-Range Order for the chirally charged fermion-mass biline"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13075","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/2606.13075/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":"2026-06-12T01:09:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asHg7kZE9pnN2He4lInv7hlcgRXSHukIUkeuGnpNi+D9VnnUyboY9T6kK+JgTesQoT2C1F5siaqVeBWLgfM3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T16:26:06.248709Z"},"content_sha256":"94ad16081b8cce05c7ff81154b5aeb3bec058765403b27ed2ea442bca9319fcc","schema_version":"1.0","event_id":"sha256:94ad16081b8cce05c7ff81154b5aeb3bec058765403b27ed2ea442bca9319fcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/bundle.json","state_url":"https://pith.science/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/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":"2026-06-28T16:26:06Z","links":{"resolver":"https://pith.science/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C","bundle":"https://pith.science/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/bundle.json","state":"https://pith.science/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKR6CVW3VBGDOA6D3W3NTS3Q6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DKR6CVW3VBGDOA6D3W3NTS3Q6C","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":"b82c376b22810da1b2911e7ab5f8e985c39f1519a5ee3afb1688b0a5c77f9971","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T08:59:34Z","title_canon_sha256":"f9ad3c4ebd567f0a113f35d4949999dec8d63ffbabc1363c6c519e245af04ae6"},"schema_version":"1.0","source":{"id":"2606.13075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13075","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13075v1","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13075","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"DKR6CVW3VBGD","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_16","alias_value":"DKR6CVW3VBGDOA6D","created_at":"2026-06-12T01:09:39Z"},{"alias_kind":"pith_short_8","alias_value":"DKR6CVW3","created_at":"2026-06-12T01:09:39Z"}],"graph_snapshots":[{"event_id":"sha256:94ad16081b8cce05c7ff81154b5aeb3bec058765403b27ed2ea442bca9319fcc","target":"graph","created_at":"2026-06-12T01:09:39Z","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/2606.13075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of Long-Range Order in a class of two-dimensional Euclidean lattice Gross-Neveu models with an even number of fermion flavors, covering three standard lattice discretizations, including naive and staggered fermions widely used in numerical studies. By performing a Hubbard-Stratonovich transformation, we map the fermionic systems to bosonic ones and establish Reflection Positivity for the resulting measures. Exploiting this structure, we combine Chessboard Estimates with a Peierls-type contour argument to prove Long-Range Order for the chirally charged fermion-mass biline","authors_text":"Leonardo Goller, Simone Fabbri","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T08:59:34Z","title":"Chiral Long-Range Order in three Euclidean Lattice Gross-Neveu Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13075","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":"sha256:770150d7c89440d5adcf9620f60d29abdacd5d7d2f77e6bc231ad5e42509bba1","target":"record","created_at":"2026-06-12T01:09:39Z","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":"b82c376b22810da1b2911e7ab5f8e985c39f1519a5ee3afb1688b0a5c77f9971","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T08:59:34Z","title_canon_sha256":"f9ad3c4ebd567f0a113f35d4949999dec8d63ffbabc1363c6c519e245af04ae6"},"schema_version":"1.0","source":{"id":"2606.13075","kind":"arxiv","version":1}},"canonical_sha256":"1aa3e156dba84c3703c3ddb6d9cb70f0bd095d9350c93934e9481f5de5f0a9d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aa3e156dba84c3703c3ddb6d9cb70f0bd095d9350c93934e9481f5de5f0a9d9","first_computed_at":"2026-06-12T01:09:39.302673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:39.302673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eCeOTD8vh7gEplQKaRQfkN1aIZ/JEguEGbQ3ijoIXgzKNYkIM7HaM7zFfjDtuDzzhZDkdDLLQf+GQkTtGgjhAg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:39.303122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:770150d7c89440d5adcf9620f60d29abdacd5d7d2f77e6bc231ad5e42509bba1","sha256:94ad16081b8cce05c7ff81154b5aeb3bec058765403b27ed2ea442bca9319fcc"],"state_sha256":"edd287bf7af9815837b7b06889aa3ee05a68732d7b5010bc1c680a75fa0e52f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MO3FzpveR5T5VBrExcUDMgICdvESES7F5LKAEzKWlmOB57v/gxyQW/sgUOjduKBDAJ7jgRdJhnooRXl0ApqSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T16:26:06.250599Z","bundle_sha256":"bbfd51caa63d7f2f90941ef38a025a42084b781549b46aff617ee3ceaf61e450"}}