{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VZVWAEME6YNKOKTWJWUEE37XS5","short_pith_number":"pith:VZVWAEME","canonical_record":{"source":{"id":"1103.3227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T16:42:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"533864ccd5c536036cf7bff4ee3f5ff8d4558bb49f050df9a2b2809afea4a8e6","abstract_canon_sha256":"9291bfbbe2eb3e174a63c62da84ec6bdcc4b42fc8590d8ef9fbdd9e29778ba62"},"schema_version":"1.0"},"canonical_sha256":"ae6b601184f61aa72a764da8426ff7977254efef976e22dc6e5ec63500d6eeb8","source":{"kind":"arxiv","id":"1103.3227","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3227","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3227v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3227","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"VZVWAEME6YNK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZVWAEME6YNKOKTW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZVWAEME","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VZVWAEME6YNKOKTWJWUEE37XS5","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T16:42:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"533864ccd5c536036cf7bff4ee3f5ff8d4558bb49f050df9a2b2809afea4a8e6","abstract_canon_sha256":"9291bfbbe2eb3e174a63c62da84ec6bdcc4b42fc8590d8ef9fbdd9e29778ba62"},"schema_version":"1.0"},"canonical_sha256":"ae6b601184f61aa72a764da8426ff7977254efef976e22dc6e5ec63500d6eeb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:44.561002Z","signature_b64":"JSrDpiACvlhJQed5kcb2DExlGOxsg+Cggz7z20u4wIkHxuQ0VfpONQSLxEiA8BVkffx/ABBIrWx+2M0uEKCqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae6b601184f61aa72a764da8426ff7977254efef976e22dc6e5ec63500d6eeb8","last_reissued_at":"2026-05-18T04:26:44.560420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:44.560420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3227","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":"2026-05-18T04:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVv6WRLEz2onmMS5uDRq3Rl09xTVYjE9p9+sofiibv5eWcy+gewDmS6Bd1O+AIEKVhhdeRnCw0YOIvSkwyCLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:18:22.932543Z"},"content_sha256":"9d1310d8b114ec3f2aef2ce7d663ae35597da55b24e4696cea6990a3a5a43f89","schema_version":"1.0","event_id":"sha256:9d1310d8b114ec3f2aef2ce7d663ae35597da55b24e4696cea6990a3a5a43f89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VZVWAEME6YNKOKTWJWUEE37XS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How is spontaneous symmetry breaking possible?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David John Baker, Hans Halvorson","submitted_at":"2011-03-16T16:42:36Z","abstract_excerpt":"We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for phys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3227","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":"2026-05-18T04:26:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDcYRKs5Qru1IVgYL8B9OuJJ82pFe8tc1XFaUmm2D1bEvoskTQ0EbPMdMaakyki4pVYjPlC/r1T7R4mwz6TFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:18:22.933216Z"},"content_sha256":"74a0bbaa8876fc2e4e8a71ff1d334a6c81f16af4ce4fa5a31928fb3b8b092755","schema_version":"1.0","event_id":"sha256:74a0bbaa8876fc2e4e8a71ff1d334a6c81f16af4ce4fa5a31928fb3b8b092755"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZVWAEME6YNKOKTWJWUEE37XS5/bundle.json","state_url":"https://pith.science/pith/VZVWAEME6YNKOKTWJWUEE37XS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZVWAEME6YNKOKTWJWUEE37XS5/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":"2026-05-26T22:18:22Z","links":{"resolver":"https://pith.science/pith/VZVWAEME6YNKOKTWJWUEE37XS5","bundle":"https://pith.science/pith/VZVWAEME6YNKOKTWJWUEE37XS5/bundle.json","state":"https://pith.science/pith/VZVWAEME6YNKOKTWJWUEE37XS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZVWAEME6YNKOKTWJWUEE37XS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VZVWAEME6YNKOKTWJWUEE37XS5","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":"9291bfbbe2eb3e174a63c62da84ec6bdcc4b42fc8590d8ef9fbdd9e29778ba62","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T16:42:36Z","title_canon_sha256":"533864ccd5c536036cf7bff4ee3f5ff8d4558bb49f050df9a2b2809afea4a8e6"},"schema_version":"1.0","source":{"id":"1103.3227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3227","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3227v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3227","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"VZVWAEME6YNK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZVWAEME6YNKOKTW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZVWAEME","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:74a0bbaa8876fc2e4e8a71ff1d334a6c81f16af4ce4fa5a31928fb3b8b092755","target":"graph","created_at":"2026-05-18T04:26:44Z","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":"We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for phys","authors_text":"David John Baker, Hans Halvorson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T16:42:36Z","title":"How is spontaneous symmetry breaking possible?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3227","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":"sha256:9d1310d8b114ec3f2aef2ce7d663ae35597da55b24e4696cea6990a3a5a43f89","target":"record","created_at":"2026-05-18T04:26:44Z","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":"9291bfbbe2eb3e174a63c62da84ec6bdcc4b42fc8590d8ef9fbdd9e29778ba62","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-16T16:42:36Z","title_canon_sha256":"533864ccd5c536036cf7bff4ee3f5ff8d4558bb49f050df9a2b2809afea4a8e6"},"schema_version":"1.0","source":{"id":"1103.3227","kind":"arxiv","version":1}},"canonical_sha256":"ae6b601184f61aa72a764da8426ff7977254efef976e22dc6e5ec63500d6eeb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae6b601184f61aa72a764da8426ff7977254efef976e22dc6e5ec63500d6eeb8","first_computed_at":"2026-05-18T04:26:44.560420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:44.560420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JSrDpiACvlhJQed5kcb2DExlGOxsg+Cggz7z20u4wIkHxuQ0VfpONQSLxEiA8BVkffx/ABBIrWx+2M0uEKCqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:44.561002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d1310d8b114ec3f2aef2ce7d663ae35597da55b24e4696cea6990a3a5a43f89","sha256:74a0bbaa8876fc2e4e8a71ff1d334a6c81f16af4ce4fa5a31928fb3b8b092755"],"state_sha256":"1d0910483ec9ce07e03b73147cd40c2676ef27b3705b2a1f0800e43bfb6a9563"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pfdq0PaEmJX9nAE/tp1tqX/tM9y+St5FP7ePuL0SbjM3+gYOpPBywNTcjx9Zz7PqtJfOk/gWKvVORRNO5i0TAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:18:22.936842Z","bundle_sha256":"89a7e3426cdbc32686c22296d462769284ed7a9e28a07bf2bba04f9642d7dbac"}}