{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2H3ZE6GV4HUGVT6IXUZUO4PC4N","short_pith_number":"pith:2H3ZE6GV","canonical_record":{"source":{"id":"1203.1494","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-07T15:17:53Z","cross_cats_sorted":["cond-mat.other","hep-ph"],"title_canon_sha256":"3f6e5f3c2756c1c5b7a7e23268ba335edf979589670cc5b0c10b24440eea5439","abstract_canon_sha256":"aa5a8aad43e8cef0a9c6a4777ff634d22a6169727e2a0858db17840a3eb1e910"},"schema_version":"1.0"},"canonical_sha256":"d1f79278d5e1e86acfc8bd334771e2e36db839edf33260828e24206125acf880","source":{"kind":"arxiv","id":"1203.1494","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1494","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1494v3","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1494","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"2H3ZE6GV4HUG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2H3ZE6GV4HUGVT6I","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2H3ZE6GV","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2H3ZE6GV4HUGVT6IXUZUO4PC4N","target":"record","payload":{"canonical_record":{"source":{"id":"1203.1494","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-07T15:17:53Z","cross_cats_sorted":["cond-mat.other","hep-ph"],"title_canon_sha256":"3f6e5f3c2756c1c5b7a7e23268ba335edf979589670cc5b0c10b24440eea5439","abstract_canon_sha256":"aa5a8aad43e8cef0a9c6a4777ff634d22a6169727e2a0858db17840a3eb1e910"},"schema_version":"1.0"},"canonical_sha256":"d1f79278d5e1e86acfc8bd334771e2e36db839edf33260828e24206125acf880","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:17.803680Z","signature_b64":"bh0fxnW899jqxjHebbAlVKOkhv7MBPrOeMWeWAYcmvf/oI6vYeL2WEpBDTpBdcMK9BqAivYtcxB1B2wnF2oXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1f79278d5e1e86acfc8bd334771e2e36db839edf33260828e24206125acf880","last_reissued_at":"2026-05-18T03:31:17.802944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:17.802944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.1494","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p/EzsZFzhcqtAbsH8xPVyN6ZEoVDDhWydKi1Dqnx0OspYfHr/1mjr7ZBaBEt3UionqrVJFD9mNlKFzY4biTHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:56:49.183776Z"},"content_sha256":"2ea79576531e6e41ab710281932648ac33c360936a6294e26be777696f329486","schema_version":"1.0","event_id":"sha256:2ea79576531e6e41ab710281932648ac33c360936a6294e26be777696f329486"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2H3ZE6GV4HUGVT6IXUZUO4PC4N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting rule for Nambu-Goldstone modes in nonrelativistic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","hep-ph"],"primary_cat":"hep-th","authors_text":"Yoshimasa Hidaka","submitted_at":"2012-03-07T15:17:53Z","abstract_excerpt":"The counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q_a, minus half the rank of the expectation value of [Q_a,Q_b]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1494","kind":"arxiv","version":3},"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":"2026-05-18T03:31:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+jtAOvbg/XTiXwXnXmQdUB4nWDvWFWaSRHvjB3k12SNhO99v2ApTcfWoGvvWfXZTjZEhm1qV7IVmDbdtD4vDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T09:56:49.184115Z"},"content_sha256":"6a4287ad460a7670e658b0137a03e4deff5a3aab064359bdaa5a28faba9075b0","schema_version":"1.0","event_id":"sha256:6a4287ad460a7670e658b0137a03e4deff5a3aab064359bdaa5a28faba9075b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/bundle.json","state_url":"https://pith.science/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/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":"2026-06-29T09:56:49Z","links":{"resolver":"https://pith.science/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N","bundle":"https://pith.science/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/bundle.json","state":"https://pith.science/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2H3ZE6GV4HUGVT6IXUZUO4PC4N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2H3ZE6GV4HUGVT6IXUZUO4PC4N","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":"aa5a8aad43e8cef0a9c6a4777ff634d22a6169727e2a0858db17840a3eb1e910","cross_cats_sorted":["cond-mat.other","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-07T15:17:53Z","title_canon_sha256":"3f6e5f3c2756c1c5b7a7e23268ba335edf979589670cc5b0c10b24440eea5439"},"schema_version":"1.0","source":{"id":"1203.1494","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1494","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1494v3","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1494","created_at":"2026-05-18T03:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"2H3ZE6GV4HUG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2H3ZE6GV4HUGVT6I","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2H3ZE6GV","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:6a4287ad460a7670e658b0137a03e4deff5a3aab064359bdaa5a28faba9075b0","target":"graph","created_at":"2026-05-18T03:31:17Z","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 counting rule for Nambu-Goldstone modes is discussed using Mori's projection operator method in nonrelativistic systems at zero and finite temperatures. We show that the number of Nambu-Goldstone modes is equal to the number of broken charges, Q_a, minus half the rank of the expectation value of [Q_a,Q_b].","authors_text":"Yoshimasa Hidaka","cross_cats":["cond-mat.other","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-07T15:17:53Z","title":"Counting rule for Nambu-Goldstone modes in nonrelativistic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1494","kind":"arxiv","version":3},"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":"sha256:2ea79576531e6e41ab710281932648ac33c360936a6294e26be777696f329486","target":"record","created_at":"2026-05-18T03:31:17Z","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":"aa5a8aad43e8cef0a9c6a4777ff634d22a6169727e2a0858db17840a3eb1e910","cross_cats_sorted":["cond-mat.other","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-07T15:17:53Z","title_canon_sha256":"3f6e5f3c2756c1c5b7a7e23268ba335edf979589670cc5b0c10b24440eea5439"},"schema_version":"1.0","source":{"id":"1203.1494","kind":"arxiv","version":3}},"canonical_sha256":"d1f79278d5e1e86acfc8bd334771e2e36db839edf33260828e24206125acf880","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1f79278d5e1e86acfc8bd334771e2e36db839edf33260828e24206125acf880","first_computed_at":"2026-05-18T03:31:17.802944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:17.802944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bh0fxnW899jqxjHebbAlVKOkhv7MBPrOeMWeWAYcmvf/oI6vYeL2WEpBDTpBdcMK9BqAivYtcxB1B2wnF2oXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:17.803680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1494","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ea79576531e6e41ab710281932648ac33c360936a6294e26be777696f329486","sha256:6a4287ad460a7670e658b0137a03e4deff5a3aab064359bdaa5a28faba9075b0"],"state_sha256":"c1e046131a1222e635dc3b604f5e650427eb2f7cf6b217905f9bd14777d78e29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VJN35wHW3yVyRb0oYVjI5+Qp/4eiQ3uI8nyi+XiDPondfvyoD9gkUrKMmWuT1PZje1XfSyGPRCsxIg37cydCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T09:56:49.186067Z","bundle_sha256":"b373e0df670196d679f2c336b27a0e05f4a1ba37a1a477cf27c9310f65effa00"}}