{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:SIKRDCV5656LGGUYPDS5WJX5V6","short_pith_number":"pith:SIKRDCV5","canonical_record":{"source":{"id":"math-ph/0611017","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-11-08T15:15:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2cc73bc095470abad983f847c3dd94c87eaeb64d770dde4a62f7a77d14eae278","abstract_canon_sha256":"88820544914587d1b613812d3a04bc804a0d6249c57967a04f00056b0d3acb22"},"schema_version":"1.0"},"canonical_sha256":"9215118abdf77cb31a9878e5db26fdafa9fa619de16678fcb9c34caf5029086f","source":{"kind":"arxiv","id":"math-ph/0611017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611017","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611017v1","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611017","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"SIKRDCV5656L","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"SIKRDCV5656LGGUY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"SIKRDCV5","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:SIKRDCV5656LGGUYPDS5WJX5V6","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0611017","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-11-08T15:15:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2cc73bc095470abad983f847c3dd94c87eaeb64d770dde4a62f7a77d14eae278","abstract_canon_sha256":"88820544914587d1b613812d3a04bc804a0d6249c57967a04f00056b0d3acb22"},"schema_version":"1.0"},"canonical_sha256":"9215118abdf77cb31a9878e5db26fdafa9fa619de16678fcb9c34caf5029086f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:32.541676Z","signature_b64":"s+sQjXMcqbkf3HGquIzQAyWmFnodOaNHcteAjPwH45Qut8Wk/Y2yTZB8KbBMM8J+PqUVuJhhAV+ZjqjK7G9qAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9215118abdf77cb31a9878e5db26fdafa9fa619de16678fcb9c34caf5029086f","last_reissued_at":"2026-05-18T01:38:32.541117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:32.541117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0611017","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":"2026-05-18T01:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9G1YMPagNgNSkIs+h0ST/2DYOEERCXPOOwHA321KriGjBJQbeVZDFRYC0c938oRYvrGgKdq79opU4gTGR2EDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:06:54.255766Z"},"content_sha256":"133ae675518740c0100932356d6b21d86b2e2e6554231dfc05a753c602fe4345","schema_version":"1.0","event_id":"sha256:133ae675518740c0100932356d6b21d86b2e2e6554231dfc05a753c602fe4345"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:SIKRDCV5656LGGUYPDS5WJX5V6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Phase Transition in a Quantum Crystal with Asymmetric Potentials","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alina Kargol, Yuri Kozitsky","submitted_at":"2006-11-08T15:15:59Z","abstract_excerpt":"A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\\geq 3$, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611017","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":"2026-05-18T01:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awhDJCaZ6TXbZDFW67dcT26UuWa9pTyF59iI/THKvbhgoZNcMWTn9Fdqbrj+3cEliS4Ks9oebMlppGnZ3mEEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:06:54.256484Z"},"content_sha256":"3680d765df85e1405b7a5dc415921a31ada7e41a0e61d6b98bbed26ae402cf97","schema_version":"1.0","event_id":"sha256:3680d765df85e1405b7a5dc415921a31ada7e41a0e61d6b98bbed26ae402cf97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIKRDCV5656LGGUYPDS5WJX5V6/bundle.json","state_url":"https://pith.science/pith/SIKRDCV5656LGGUYPDS5WJX5V6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIKRDCV5656LGGUYPDS5WJX5V6/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":"2026-05-31T23:06:54Z","links":{"resolver":"https://pith.science/pith/SIKRDCV5656LGGUYPDS5WJX5V6","bundle":"https://pith.science/pith/SIKRDCV5656LGGUYPDS5WJX5V6/bundle.json","state":"https://pith.science/pith/SIKRDCV5656LGGUYPDS5WJX5V6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIKRDCV5656LGGUYPDS5WJX5V6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:SIKRDCV5656LGGUYPDS5WJX5V6","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":"88820544914587d1b613812d3a04bc804a0d6249c57967a04f00056b0d3acb22","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-11-08T15:15:59Z","title_canon_sha256":"2cc73bc095470abad983f847c3dd94c87eaeb64d770dde4a62f7a77d14eae278"},"schema_version":"1.0","source":{"id":"math-ph/0611017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611017","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611017v1","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611017","created_at":"2026-05-18T01:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"SIKRDCV5656L","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"SIKRDCV5656LGGUY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"SIKRDCV5","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:3680d765df85e1405b7a5dc415921a31ada7e41a0e61d6b98bbed26ae402cf97","target":"graph","created_at":"2026-05-18T01:38:32Z","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":"A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\\geq 3$, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and","authors_text":"Alina Kargol, Yuri Kozitsky","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2006-11-08T15:15:59Z","title":"A Phase Transition in a Quantum Crystal with Asymmetric Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611017","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":"sha256:133ae675518740c0100932356d6b21d86b2e2e6554231dfc05a753c602fe4345","target":"record","created_at":"2026-05-18T01:38:32Z","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":"88820544914587d1b613812d3a04bc804a0d6249c57967a04f00056b0d3acb22","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2006-11-08T15:15:59Z","title_canon_sha256":"2cc73bc095470abad983f847c3dd94c87eaeb64d770dde4a62f7a77d14eae278"},"schema_version":"1.0","source":{"id":"math-ph/0611017","kind":"arxiv","version":1}},"canonical_sha256":"9215118abdf77cb31a9878e5db26fdafa9fa619de16678fcb9c34caf5029086f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9215118abdf77cb31a9878e5db26fdafa9fa619de16678fcb9c34caf5029086f","first_computed_at":"2026-05-18T01:38:32.541117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:32.541117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s+sQjXMcqbkf3HGquIzQAyWmFnodOaNHcteAjPwH45Qut8Wk/Y2yTZB8KbBMM8J+PqUVuJhhAV+ZjqjK7G9qAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:32.541676Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0611017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:133ae675518740c0100932356d6b21d86b2e2e6554231dfc05a753c602fe4345","sha256:3680d765df85e1405b7a5dc415921a31ada7e41a0e61d6b98bbed26ae402cf97"],"state_sha256":"08932d2eb4a716ad0128eba3c4efca3439bf73359d16a1eb7052cab373107c52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFMu4u8wC2DajLR29NKd2EdutSMCZQ8u3CeoiZdmW2UZevW6Lt9SCiicbDp7PQ4yeaksLVD7kkY4bVGF5p48BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:06:54.260477Z","bundle_sha256":"4296a070400e62d962b2854fb6e35373f10cd71006cebcec26d446338afa04cc"}}