{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3TSLXM4NV6GDIC25JCVUKWZPFD","short_pith_number":"pith:3TSLXM4N","canonical_record":{"source":{"id":"1301.2562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-11T18:01:39Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"10f82746d16c41fce0a1081dc27e2fffd4cde596b8848fb7ceeebe1cb3eed1d1","abstract_canon_sha256":"65c6558fd6e19912655b1be2cb7e944513cec3bde9b181f6e8ee1efec126a572"},"schema_version":"1.0"},"canonical_sha256":"dce4bbb38daf8c340b5d48ab455b2f28d4c1927ea9690b78ea4383d7d4af4fcc","source":{"kind":"arxiv","id":"1301.2562","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2562","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2562v2","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2562","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"3TSLXM4NV6GD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TSLXM4NV6GDIC25","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TSLXM4N","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3TSLXM4NV6GDIC25JCVUKWZPFD","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-11T18:01:39Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"10f82746d16c41fce0a1081dc27e2fffd4cde596b8848fb7ceeebe1cb3eed1d1","abstract_canon_sha256":"65c6558fd6e19912655b1be2cb7e944513cec3bde9b181f6e8ee1efec126a572"},"schema_version":"1.0"},"canonical_sha256":"dce4bbb38daf8c340b5d48ab455b2f28d4c1927ea9690b78ea4383d7d4af4fcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:12.892948Z","signature_b64":"XVMa3E1AsJzM51ujloxPGI8Cuif41ZtNZDLZibTaN/klO0NxtDoFf0/u4sew+X+i8FKpdkSTvZCNCMZlfDwRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dce4bbb38daf8c340b5d48ab455b2f28d4c1927ea9690b78ea4383d7d4af4fcc","last_reissued_at":"2026-05-18T03:09:12.892537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:12.892537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2562","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YOJcau3WPEY6ZkNz7k2Ff7stBFXvIsZgQH87NQtdpmdXyJBr/K9PEx6DcNSgzSmo92McaPoLJfKUVOJnfKEAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:28:42.961131Z"},"content_sha256":"25793b04e7dd631e3bcc5153301a829c523cd180c84820531190783fbee27ceb","schema_version":"1.0","event_id":"sha256:25793b04e7dd631e3bcc5153301a829c523cd180c84820531190783fbee27ceb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3TSLXM4NV6GDIC25JCVUKWZPFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bosonic Fields in Crystal Manyfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"G. Alencar, M. O. Tahim, R.N. Costa Filho, R. R. Landim","submitted_at":"2013-01-11T18:01:39Z","abstract_excerpt":"A chain-like or a 1D crystal-like universe made of intersecting membranes in extra dimensions in a Randall-Sundrum scenario is studied. A background gravitational metric satisfying the right boundary conditions is considered to study the localization of the scalar, gauge and Kalb-Ramond field. It is found that the wave function for the fields are Bloch waves. The mass modes equations are calculated allowing us to show the zero-gap mass behavior and the mass dispersion relation for each field. Finally we generalize all these results and consider $q-$forms in the crystal membrane universe. We sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2562","kind":"arxiv","version":2},"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":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKTfaI6JlixMkOJ2YC48YEz2Z8sOyhkl/sTPBoZyuC+oI56ygsTlRv+8NqyCm2mTQbDqBGgdmzt+prfBhksmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:28:42.961662Z"},"content_sha256":"f324139bd33445c1445132e00d042c2bdc81b042493ce8c70494ce0350cb4db9","schema_version":"1.0","event_id":"sha256:f324139bd33445c1445132e00d042c2bdc81b042493ce8c70494ce0350cb4db9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/bundle.json","state_url":"https://pith.science/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/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":"2026-06-01T17:28:42Z","links":{"resolver":"https://pith.science/pith/3TSLXM4NV6GDIC25JCVUKWZPFD","bundle":"https://pith.science/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/bundle.json","state":"https://pith.science/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TSLXM4NV6GDIC25JCVUKWZPFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3TSLXM4NV6GDIC25JCVUKWZPFD","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":"65c6558fd6e19912655b1be2cb7e944513cec3bde9b181f6e8ee1efec126a572","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-11T18:01:39Z","title_canon_sha256":"10f82746d16c41fce0a1081dc27e2fffd4cde596b8848fb7ceeebe1cb3eed1d1"},"schema_version":"1.0","source":{"id":"1301.2562","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2562","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2562v2","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2562","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"3TSLXM4NV6GD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TSLXM4NV6GDIC25","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TSLXM4N","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:f324139bd33445c1445132e00d042c2bdc81b042493ce8c70494ce0350cb4db9","target":"graph","created_at":"2026-05-18T03:09:12Z","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 chain-like or a 1D crystal-like universe made of intersecting membranes in extra dimensions in a Randall-Sundrum scenario is studied. A background gravitational metric satisfying the right boundary conditions is considered to study the localization of the scalar, gauge and Kalb-Ramond field. It is found that the wave function for the fields are Bloch waves. The mass modes equations are calculated allowing us to show the zero-gap mass behavior and the mass dispersion relation for each field. Finally we generalize all these results and consider $q-$forms in the crystal membrane universe. We sh","authors_text":"G. Alencar, M. O. Tahim, R.N. Costa Filho, R. R. Landim","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-11T18:01:39Z","title":"Bosonic Fields in Crystal Manyfolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2562","kind":"arxiv","version":2},"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":"sha256:25793b04e7dd631e3bcc5153301a829c523cd180c84820531190783fbee27ceb","target":"record","created_at":"2026-05-18T03:09:12Z","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":"65c6558fd6e19912655b1be2cb7e944513cec3bde9b181f6e8ee1efec126a572","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-11T18:01:39Z","title_canon_sha256":"10f82746d16c41fce0a1081dc27e2fffd4cde596b8848fb7ceeebe1cb3eed1d1"},"schema_version":"1.0","source":{"id":"1301.2562","kind":"arxiv","version":2}},"canonical_sha256":"dce4bbb38daf8c340b5d48ab455b2f28d4c1927ea9690b78ea4383d7d4af4fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dce4bbb38daf8c340b5d48ab455b2f28d4c1927ea9690b78ea4383d7d4af4fcc","first_computed_at":"2026-05-18T03:09:12.892537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:12.892537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVMa3E1AsJzM51ujloxPGI8Cuif41ZtNZDLZibTaN/klO0NxtDoFf0/u4sew+X+i8FKpdkSTvZCNCMZlfDwRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:12.892948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2562","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25793b04e7dd631e3bcc5153301a829c523cd180c84820531190783fbee27ceb","sha256:f324139bd33445c1445132e00d042c2bdc81b042493ce8c70494ce0350cb4db9"],"state_sha256":"d1f7130ea124ab95e635af96a90d9313ff87d528520fbb99efb3e9b75837e759"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrKlt4/LOaOTKbohc4TH+1lkoFPCBOkf8aFXPdod2aBuDnsLFemZwcsJQ4+Qy9xv7sKZOftgwNd4MU9eXGNKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:28:42.963743Z","bundle_sha256":"4214133fbc24d9173c62e4d487c1fdae785d259e9269adbc8cc8b7d4e4b3e930"}}