{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UAHTRY7IHXW6LENBS7Q2DC4X36","short_pith_number":"pith:UAHTRY7I","canonical_record":{"source":{"id":"1512.06838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-21T20:58:06Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"title_canon_sha256":"39e37c61e8c982a714ea4dd46e4ef42f87706f92ca1d82c3a42b27614650ad28","abstract_canon_sha256":"5ed6d6cf93e81155d025cb1f24edb9a08b7126cd791ca460133febe0b466fb3b"},"schema_version":"1.0"},"canonical_sha256":"a00f38e3e83dede591a197e1a18b97df9232618803bcb2e3cdcaff4f41d4eaba","source":{"kind":"arxiv","id":"1512.06838","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06838","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06838v2","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06838","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"UAHTRY7IHXW6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UAHTRY7IHXW6LENB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UAHTRY7I","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UAHTRY7IHXW6LENBS7Q2DC4X36","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-21T20:58:06Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"title_canon_sha256":"39e37c61e8c982a714ea4dd46e4ef42f87706f92ca1d82c3a42b27614650ad28","abstract_canon_sha256":"5ed6d6cf93e81155d025cb1f24edb9a08b7126cd791ca460133febe0b466fb3b"},"schema_version":"1.0"},"canonical_sha256":"a00f38e3e83dede591a197e1a18b97df9232618803bcb2e3cdcaff4f41d4eaba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:12.364371Z","signature_b64":"X2aMjKoHSpSDPHUJdSsJnrnWK4i7z/o2Yy7tThwLQqly9zkjQqWBC3DOIn50v1V5LChLA0EDqRIf3fatHedzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a00f38e3e83dede591a197e1a18b97df9232618803bcb2e3cdcaff4f41d4eaba","last_reissued_at":"2026-05-18T01:08:12.363933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:12.363933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06838","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6RVFT2HUGUUCAbI9lg7VsIXDaYTaEndueBiSOXmL/O2QX+P04bEyXRKAohcOzEcp5gz+qWBazLiEclLZk75cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:18:55.898733Z"},"content_sha256":"dd6ff766b2dcc0fa21b9e3798c0390c0602d8c3feaa22041ee1fa5a39ccb3922","schema_version":"1.0","event_id":"sha256:dd6ff766b2dcc0fa21b9e3798c0390c0602d8c3feaa22041ee1fa5a39ccb3922"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UAHTRY7IHXW6LENBS7Q2DC4X36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-compact nonlinear sigma models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc","hep-ph"],"primary_cat":"hep-th","authors_text":"Andrew J. Tolley, Claudia de Rham, Shuang-Yong Zhou","submitted_at":"2015-12-21T20:58:06Z","abstract_excerpt":"The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz--invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06838","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OIdI8YvmTZS8BTQIMlV3Td+8xka9mGDkUPVC41zDGMZBZBd0sVufP4YYY2/18taQSRB55ZuYWuCy1FQUg2JuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:18:55.899084Z"},"content_sha256":"5312c0e56d0636100862d3f3ef260d4cf9dcfdcc58f6c9e4a820b8d636211724","schema_version":"1.0","event_id":"sha256:5312c0e56d0636100862d3f3ef260d4cf9dcfdcc58f6c9e4a820b8d636211724"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/bundle.json","state_url":"https://pith.science/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/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":"2026-06-04T17:18:55Z","links":{"resolver":"https://pith.science/pith/UAHTRY7IHXW6LENBS7Q2DC4X36","bundle":"https://pith.science/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/bundle.json","state":"https://pith.science/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAHTRY7IHXW6LENBS7Q2DC4X36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UAHTRY7IHXW6LENBS7Q2DC4X36","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":"5ed6d6cf93e81155d025cb1f24edb9a08b7126cd791ca460133febe0b466fb3b","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-21T20:58:06Z","title_canon_sha256":"39e37c61e8c982a714ea4dd46e4ef42f87706f92ca1d82c3a42b27614650ad28"},"schema_version":"1.0","source":{"id":"1512.06838","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06838","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06838v2","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06838","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"UAHTRY7IHXW6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UAHTRY7IHXW6LENB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UAHTRY7I","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:5312c0e56d0636100862d3f3ef260d4cf9dcfdcc58f6c9e4a820b8d636211724","target":"graph","created_at":"2026-05-18T01:08:12Z","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":"The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz--invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free fr","authors_text":"Andrew J. Tolley, Claudia de Rham, Shuang-Yong Zhou","cross_cats":["astro-ph.CO","gr-qc","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-21T20:58:06Z","title":"Non-compact nonlinear sigma models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06838","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:dd6ff766b2dcc0fa21b9e3798c0390c0602d8c3feaa22041ee1fa5a39ccb3922","target":"record","created_at":"2026-05-18T01:08:12Z","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":"5ed6d6cf93e81155d025cb1f24edb9a08b7126cd791ca460133febe0b466fb3b","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-21T20:58:06Z","title_canon_sha256":"39e37c61e8c982a714ea4dd46e4ef42f87706f92ca1d82c3a42b27614650ad28"},"schema_version":"1.0","source":{"id":"1512.06838","kind":"arxiv","version":2}},"canonical_sha256":"a00f38e3e83dede591a197e1a18b97df9232618803bcb2e3cdcaff4f41d4eaba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a00f38e3e83dede591a197e1a18b97df9232618803bcb2e3cdcaff4f41d4eaba","first_computed_at":"2026-05-18T01:08:12.363933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:12.363933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X2aMjKoHSpSDPHUJdSsJnrnWK4i7z/o2Yy7tThwLQqly9zkjQqWBC3DOIn50v1V5LChLA0EDqRIf3fatHedzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:12.364371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06838","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd6ff766b2dcc0fa21b9e3798c0390c0602d8c3feaa22041ee1fa5a39ccb3922","sha256:5312c0e56d0636100862d3f3ef260d4cf9dcfdcc58f6c9e4a820b8d636211724"],"state_sha256":"d37e22b1fefa05d88d534e87c927ed30b5d98bf32b089b862c1423702391740a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3FdiF3joXjMYjVRRl8Uy3P8tM7lcLOjjWzNLbhNKAIrqDoY1ghWSqe09zWBZnNUNtFbPQQgvCN3WYuCnucwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:18:55.900996Z","bundle_sha256":"ddf4508fe2f4a8050d81a24a7aacbf2f56da4b5a833a0f46609def4e440c42fb"}}