{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OCTSZH4J47LJ3I7KZPBNQD25MI","short_pith_number":"pith:OCTSZH4J","canonical_record":{"source":{"id":"1103.3549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-18T02:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"702f50b9f931363b56e3bcfc72a52afda4e7a0e471cc4e6e93fb548f0301ec10","abstract_canon_sha256":"fc94e2d5f951152e03b4e84e035723f163c6bb7e4cd1a749d1b38e2c8cee7201"},"schema_version":"1.0"},"canonical_sha256":"70a72c9f89e7d69da3eacbc2d80f5d620dea6b3a65b70deb275a90cbb3301961","source":{"kind":"arxiv","id":"1103.3549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3549","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3549v1","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3549","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"OCTSZH4J47LJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OCTSZH4J47LJ3I7K","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OCTSZH4J","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OCTSZH4J47LJ3I7KZPBNQD25MI","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-18T02:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"702f50b9f931363b56e3bcfc72a52afda4e7a0e471cc4e6e93fb548f0301ec10","abstract_canon_sha256":"fc94e2d5f951152e03b4e84e035723f163c6bb7e4cd1a749d1b38e2c8cee7201"},"schema_version":"1.0"},"canonical_sha256":"70a72c9f89e7d69da3eacbc2d80f5d620dea6b3a65b70deb275a90cbb3301961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:50.073492Z","signature_b64":"L4XNcSYtlIZwzg6cFTgEFfAY1vtyb5/hpl+y2iC8lI0wtKXW11Hm0WunArOUxogR5En2riRHpKDvdr/CqfueCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70a72c9f89e7d69da3eacbc2d80f5d620dea6b3a65b70deb275a90cbb3301961","last_reissued_at":"2026-05-18T02:02:50.072839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:50.072839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3549","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":"2026-05-18T02:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7B6mFsrTEK0NKxV30uvDyhUaVhUm9sjTyBqbGbofiDkh3/COG8Gg7BHD8jeWSVySXvYhSqp70dv7L7hemoCxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:50:20.246519Z"},"content_sha256":"f314075e43e771e6ce5cb3867f8ebfb970062a20bc68cda94be773cb0a038726","schema_version":"1.0","event_id":"sha256:f314075e43e771e6ce5cb3867f8ebfb970062a20bc68cda94be773cb0a038726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OCTSZH4J47LJ3I7KZPBNQD25MI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residue theorem and summing over Kaluza-Klein excitations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Jian-Bin Chen, Ke-Sheng Sun, Tai-Fu Feng, Tie-Jun Gao","submitted_at":"2011-03-18T02:58:37Z","abstract_excerpt":"Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluze-Klein modes in framework of warped extra dimension with the custodial symmetry $SU(3)_c\\times SU(2)_L\\times SU(2)_R\\times U(1)_X\\times P_{LR}$. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3549","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":"2026-05-18T02:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W92jARl4N776Elwh87wTt7E40lW+qGc9nP4drQ+BUAkrIp4uR6Q1bwhpkBAMXxzBu5blzjtOIi8Agw9HEfZfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:50:20.246892Z"},"content_sha256":"b3a031969f00e206fa909be3d073fcff5f2a795fe148b2b37ea23098e54cf759","schema_version":"1.0","event_id":"sha256:b3a031969f00e206fa909be3d073fcff5f2a795fe148b2b37ea23098e54cf759"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/bundle.json","state_url":"https://pith.science/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/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":"2026-06-04T01:50:20Z","links":{"resolver":"https://pith.science/pith/OCTSZH4J47LJ3I7KZPBNQD25MI","bundle":"https://pith.science/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/bundle.json","state":"https://pith.science/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OCTSZH4J47LJ3I7KZPBNQD25MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OCTSZH4J47LJ3I7KZPBNQD25MI","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":"fc94e2d5f951152e03b4e84e035723f163c6bb7e4cd1a749d1b38e2c8cee7201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-18T02:58:37Z","title_canon_sha256":"702f50b9f931363b56e3bcfc72a52afda4e7a0e471cc4e6e93fb548f0301ec10"},"schema_version":"1.0","source":{"id":"1103.3549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3549","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3549v1","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3549","created_at":"2026-05-18T02:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"OCTSZH4J47LJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OCTSZH4J47LJ3I7K","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OCTSZH4J","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b3a031969f00e206fa909be3d073fcff5f2a795fe148b2b37ea23098e54cf759","target":"graph","created_at":"2026-05-18T02:02:50Z","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":"Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluze-Klein modes in framework of warped extra dimension with the custodial symmetry $SU(3)_c\\times SU(2)_L\\times SU(2)_R\\times U(1)_X\\times P_{LR}$. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infi","authors_text":"Jian-Bin Chen, Ke-Sheng Sun, Tai-Fu Feng, Tie-Jun Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-18T02:58:37Z","title":"Residue theorem and summing over Kaluza-Klein excitations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3549","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:f314075e43e771e6ce5cb3867f8ebfb970062a20bc68cda94be773cb0a038726","target":"record","created_at":"2026-05-18T02:02:50Z","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":"fc94e2d5f951152e03b4e84e035723f163c6bb7e4cd1a749d1b38e2c8cee7201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-18T02:58:37Z","title_canon_sha256":"702f50b9f931363b56e3bcfc72a52afda4e7a0e471cc4e6e93fb548f0301ec10"},"schema_version":"1.0","source":{"id":"1103.3549","kind":"arxiv","version":1}},"canonical_sha256":"70a72c9f89e7d69da3eacbc2d80f5d620dea6b3a65b70deb275a90cbb3301961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70a72c9f89e7d69da3eacbc2d80f5d620dea6b3a65b70deb275a90cbb3301961","first_computed_at":"2026-05-18T02:02:50.072839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:50.072839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L4XNcSYtlIZwzg6cFTgEFfAY1vtyb5/hpl+y2iC8lI0wtKXW11Hm0WunArOUxogR5En2riRHpKDvdr/CqfueCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:50.073492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f314075e43e771e6ce5cb3867f8ebfb970062a20bc68cda94be773cb0a038726","sha256:b3a031969f00e206fa909be3d073fcff5f2a795fe148b2b37ea23098e54cf759"],"state_sha256":"6c7f42f82225ab328213955de023f11f33ab5854d17b5ca5692bb38a8fc38be0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5joutyjJBnUvFVRkV3ud1PYXhXoKqMWGGhIiBu5s1nOjvNCbwmdZWdl0s7qbAGwBKgtk8w/RMRk6AiwcaMZXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:50:20.249042Z","bundle_sha256":"06287a2ede66fff5a8b0227ee92ebf237926e11e8661a1c1eae04faf10aab43a"}}