{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:KA3GEQA6TVZZWHFCT4OUGY5YRG","short_pith_number":"pith:KA3GEQA6","schema_version":"1.0","canonical_sha256":"503662401e9d739b1ca29f1d4363b889af96d0c02e377ded3a9637091d016897","source":{"kind":"arxiv","id":"2110.14504","version":1},"attestation_state":"computed","paper":{"title":"An introduction to Goldstone boson physics and to the coset construction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.other","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Daniel Naegels","submitted_at":"2021-10-27T15:16:45Z","abstract_excerpt":"These lecture notes are based on a six-hour series of lectures given at the XVII Modave summer school in mathematical physics, aimed at Ph.D. students in high-energy theoretical physics.\n  The manuscript starts by briefly stating Goldstone's theorem and emphasises the motivations behind Goldstone physics; the main asset being the universality of spontaneous symmetry breaking (SSB) which is the fundamental hypothesis of Goldstone's theorem. Once the different notions of SSB will be clarified/reviewed, Goldstone's theorem will be stated and proved. A prediction of this theorem is the existence o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.14504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-27T15:16:45Z","cross_cats_sorted":["cond-mat.other","hep-ph","math-ph","math.MP"],"title_canon_sha256":"3fd6fc6738b1e870fcf46435b00357705463020d170ddd6ef65b89a86ef99812","abstract_canon_sha256":"53c1302a212045b6ad08e1044167e83a9ebfb77fc0c24d888f7bca85961119e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:28.448921Z","signature_b64":"oO1JL39fVsoXoWiQBfQZftIImRZcfXoVS0aRuBWjn5sIEGirtpzFYWPr3mfrntgYXoDi+/Z1qZmh6VhnJwLeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503662401e9d739b1ca29f1d4363b889af96d0c02e377ded3a9637091d016897","last_reissued_at":"2026-07-05T03:26:28.448521Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:28.448521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An introduction to Goldstone boson physics and to the coset construction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.other","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Daniel Naegels","submitted_at":"2021-10-27T15:16:45Z","abstract_excerpt":"These lecture notes are based on a six-hour series of lectures given at the XVII Modave summer school in mathematical physics, aimed at Ph.D. students in high-energy theoretical physics.\n  The manuscript starts by briefly stating Goldstone's theorem and emphasises the motivations behind Goldstone physics; the main asset being the universality of spontaneous symmetry breaking (SSB) which is the fundamental hypothesis of Goldstone's theorem. Once the different notions of SSB will be clarified/reviewed, Goldstone's theorem will be stated and proved. A prediction of this theorem is the existence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14504","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/2110.14504/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.14504","created_at":"2026-07-05T03:26:28.448583+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.14504v1","created_at":"2026-07-05T03:26:28.448583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14504","created_at":"2026-07-05T03:26:28.448583+00:00"},{"alias_kind":"pith_short_12","alias_value":"KA3GEQA6TVZZ","created_at":"2026-07-05T03:26:28.448583+00:00"},{"alias_kind":"pith_short_16","alias_value":"KA3GEQA6TVZZWHFC","created_at":"2026-07-05T03:26:28.448583+00:00"},{"alias_kind":"pith_short_8","alias_value":"KA3GEQA6","created_at":"2026-07-05T03:26:28.448583+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.19619","citing_title":"SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows","ref_index":73,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG","json":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG.json","graph_json":"https://pith.science/api/pith-number/KA3GEQA6TVZZWHFCT4OUGY5YRG/graph.json","events_json":"https://pith.science/api/pith-number/KA3GEQA6TVZZWHFCT4OUGY5YRG/events.json","paper":"https://pith.science/paper/KA3GEQA6"},"agent_actions":{"view_html":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG","download_json":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG.json","view_paper":"https://pith.science/paper/KA3GEQA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.14504&json=true","fetch_graph":"https://pith.science/api/pith-number/KA3GEQA6TVZZWHFCT4OUGY5YRG/graph.json","fetch_events":"https://pith.science/api/pith-number/KA3GEQA6TVZZWHFCT4OUGY5YRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG/action/storage_attestation","attest_author":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG/action/author_attestation","sign_citation":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG/action/citation_signature","submit_replication":"https://pith.science/pith/KA3GEQA6TVZZWHFCT4OUGY5YRG/action/replication_record"}},"created_at":"2026-07-05T03:26:28.448583+00:00","updated_at":"2026-07-05T03:26:28.448583+00:00"}