{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:HNT76UDTAGN7HAQAELYTVIHL35","short_pith_number":"pith:HNT76UDT","canonical_record":{"source":{"id":"hep-th/9512200","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-12-27T01:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"073bef6cbd5debf7a916fc14e862deb18b8c4141c8141dab887a015cec5c0868","abstract_canon_sha256":"bc8163b2364154c73176d8e7859f394e2411a230bdc0489c0e79fb567f13faa3"},"schema_version":"1.0"},"canonical_sha256":"3b67ff5073019bf3820022f13aa0ebdf5b9d67fb93c122c84fae41d2d3af54a6","source":{"kind":"arxiv","id":"hep-th/9512200","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9512200","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9512200v1","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9512200","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"HNT76UDTAGN7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"HNT76UDTAGN7HAQA","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"HNT76UDT","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:HNT76UDTAGN7HAQAELYTVIHL35","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9512200","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-12-27T01:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"073bef6cbd5debf7a916fc14e862deb18b8c4141c8141dab887a015cec5c0868","abstract_canon_sha256":"bc8163b2364154c73176d8e7859f394e2411a230bdc0489c0e79fb567f13faa3"},"schema_version":"1.0"},"canonical_sha256":"3b67ff5073019bf3820022f13aa0ebdf5b9d67fb93c122c84fae41d2d3af54a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:38.456571Z","signature_b64":"xQwX9Z1JPgOlL+X5slRL9NDhKywHM+vduP+cRsCd8Irpty2gLmyEHPT1a0O8l6AdCijhd2emd8X0rQh2XFOfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b67ff5073019bf3820022f13aa0ebdf5b9d67fb93c122c84fae41d2d3af54a6","last_reissued_at":"2026-05-18T01:38:38.456061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:38.456061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9512200","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":"2026-05-18T01:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PP4SEhKNm5V9UCeFzrMyan/4KWf6cFTjtZ27OSerDfUfFiVgoFH0hIviXz71PuIeqbvkhsXVF6Po/b7PyH5FBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:06:46.557731Z"},"content_sha256":"8c4fe34d36b4a1c6b3b430281a2dcf27bf5c39ec1053bc7d9d7091cd0d07652a","schema_version":"1.0","event_id":"sha256:8c4fe34d36b4a1c6b3b430281a2dcf27bf5c39ec1053bc7d9d7091cd0d07652a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:HNT76UDTAGN7HAQAELYTVIHL35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature Induced Phase Transition in a Four-Fermion Theory Using the Weak Curvature Expansion","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Tomohiro Inagaki","submitted_at":"1995-12-27T01:01:26Z","abstract_excerpt":"Curvature induced phase transition is thoroughly investigated in a four- fermion theory with $N$ components of fermions for arbitrary space-time dimensions $(2 \\leq D < 4)$. We adopt the $1/N$ expansion method and calculate the effective potential for a composite operator $\\bar{\\psi}\\psi$. The resulting effective potential is expanded asymptotically in terms of the space-time curvature $R$ by using the Riemann normal coordinate. We assume that the space-time curves slowly and keep only terms independent of $R$ and terms linear in $R$. Evaluating the effective potential it is found that the fir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9512200","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":"2026-05-18T01:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMQFsaQDZgsj0bL5xidMz3V9hLhTVldtKXQ7owHAJteUYd8DZ+i5FBjxaCqsPspekDyjuQTsN0XHxbgzAb4PDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:06:46.558084Z"},"content_sha256":"d1207c3fa665973a4e00c88159daebe8a53e685ed1c8d1602f3e8d5788903de5","schema_version":"1.0","event_id":"sha256:d1207c3fa665973a4e00c88159daebe8a53e685ed1c8d1602f3e8d5788903de5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNT76UDTAGN7HAQAELYTVIHL35/bundle.json","state_url":"https://pith.science/pith/HNT76UDTAGN7HAQAELYTVIHL35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNT76UDTAGN7HAQAELYTVIHL35/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":"2026-06-04T23:06:46Z","links":{"resolver":"https://pith.science/pith/HNT76UDTAGN7HAQAELYTVIHL35","bundle":"https://pith.science/pith/HNT76UDTAGN7HAQAELYTVIHL35/bundle.json","state":"https://pith.science/pith/HNT76UDTAGN7HAQAELYTVIHL35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNT76UDTAGN7HAQAELYTVIHL35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:HNT76UDTAGN7HAQAELYTVIHL35","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":"bc8163b2364154c73176d8e7859f394e2411a230bdc0489c0e79fb567f13faa3","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1995-12-27T01:01:26Z","title_canon_sha256":"073bef6cbd5debf7a916fc14e862deb18b8c4141c8141dab887a015cec5c0868"},"schema_version":"1.0","source":{"id":"hep-th/9512200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9512200","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9512200v1","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9512200","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"HNT76UDTAGN7","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"HNT76UDTAGN7HAQA","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"HNT76UDT","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:d1207c3fa665973a4e00c88159daebe8a53e685ed1c8d1602f3e8d5788903de5","target":"graph","created_at":"2026-05-18T01:38:38Z","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":"Curvature induced phase transition is thoroughly investigated in a four- fermion theory with $N$ components of fermions for arbitrary space-time dimensions $(2 \\leq D < 4)$. We adopt the $1/N$ expansion method and calculate the effective potential for a composite operator $\\bar{\\psi}\\psi$. The resulting effective potential is expanded asymptotically in terms of the space-time curvature $R$ by using the Riemann normal coordinate. We assume that the space-time curves slowly and keep only terms independent of $R$ and terms linear in $R$. Evaluating the effective potential it is found that the fir","authors_text":"Tomohiro Inagaki","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1995-12-27T01:01:26Z","title":"Curvature Induced Phase Transition in a Four-Fermion Theory Using the Weak Curvature Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9512200","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":"sha256:8c4fe34d36b4a1c6b3b430281a2dcf27bf5c39ec1053bc7d9d7091cd0d07652a","target":"record","created_at":"2026-05-18T01:38:38Z","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":"bc8163b2364154c73176d8e7859f394e2411a230bdc0489c0e79fb567f13faa3","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1995-12-27T01:01:26Z","title_canon_sha256":"073bef6cbd5debf7a916fc14e862deb18b8c4141c8141dab887a015cec5c0868"},"schema_version":"1.0","source":{"id":"hep-th/9512200","kind":"arxiv","version":1}},"canonical_sha256":"3b67ff5073019bf3820022f13aa0ebdf5b9d67fb93c122c84fae41d2d3af54a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b67ff5073019bf3820022f13aa0ebdf5b9d67fb93c122c84fae41d2d3af54a6","first_computed_at":"2026-05-18T01:38:38.456061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:38.456061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQwX9Z1JPgOlL+X5slRL9NDhKywHM+vduP+cRsCd8Irpty2gLmyEHPT1a0O8l6AdCijhd2emd8X0rQh2XFOfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:38.456571Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9512200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c4fe34d36b4a1c6b3b430281a2dcf27bf5c39ec1053bc7d9d7091cd0d07652a","sha256:d1207c3fa665973a4e00c88159daebe8a53e685ed1c8d1602f3e8d5788903de5"],"state_sha256":"5a481c2391b1fccb1528926418da041e5d5ff00951fdddc2156ab96efd9d4786"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avkSJjTXzxLlHR9Vp+aw2Tn3xTpeVLQGzIP0T+xf+MgiCZqQyeqnV/1MVYeqkC7rc16YfDhMmQ5gN68adHoWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:06:46.560286Z","bundle_sha256":"644fd6c50e5df424cd89e26fc17ec5e06f81657760de69a4640cf2c6413fb392"}}