{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RWZCE6YFGA47FW6UY7E4VJFTQB","short_pith_number":"pith:RWZCE6YF","canonical_record":{"source":{"id":"2506.08522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-10T07:38:57Z","cross_cats_sorted":[],"title_canon_sha256":"76f430285c721ebfe8ff594069242fe73d3d7094663f059fe3e07e749fa9095d","abstract_canon_sha256":"657984570d9523ece8152e49128aec6e4770d85a506b086e97b3eaef0d7046d5"},"schema_version":"1.0"},"canonical_sha256":"8db2227b053039f2dbd4c7c9caa4b38045890d261a0ac7220a2e0ef5766c1bfe","source":{"kind":"arxiv","id":"2506.08522","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08522","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08522v1","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08522","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"RWZCE6YFGA47","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_16","alias_value":"RWZCE6YFGA47FW6U","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_8","alias_value":"RWZCE6YF","created_at":"2026-07-05T11:18:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RWZCE6YFGA47FW6UY7E4VJFTQB","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-10T07:38:57Z","cross_cats_sorted":[],"title_canon_sha256":"76f430285c721ebfe8ff594069242fe73d3d7094663f059fe3e07e749fa9095d","abstract_canon_sha256":"657984570d9523ece8152e49128aec6e4770d85a506b086e97b3eaef0d7046d5"},"schema_version":"1.0"},"canonical_sha256":"8db2227b053039f2dbd4c7c9caa4b38045890d261a0ac7220a2e0ef5766c1bfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:51.095994Z","signature_b64":"9vqjSI7l8i5T1NQQtUwBda1HLrEHMNS8d7kgw06Kv3G/V+XCuZ0bpWvDMM2jk4DuNXNUyMhDcusEni2DNGrsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8db2227b053039f2dbd4c7c9caa4b38045890d261a0ac7220a2e0ef5766c1bfe","last_reissued_at":"2026-07-05T11:18:51.095383Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:51.095383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08522","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":"2026-07-05T11:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slr9z8wEJM5b+YpgAaGcOH20MMkrQqSeaLyWNqPDfzXJlZAcJGwx46g15DwXWP8iUCA+4dmvtL1S37BR37YsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:59:22.139486Z"},"content_sha256":"28f9b6d5f2360b4826db9d257bc40c9767da8ad73da9ca1246d6349d4e9aa132","schema_version":"1.0","event_id":"sha256:28f9b6d5f2360b4826db9d257bc40c9767da8ad73da9ca1246d6349d4e9aa132"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RWZCE6YFGA47FW6UY7E4VJFTQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonant frequencies distribution for multiple closely spaced subwavelength resonators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haigang Li, Junhua Zhang","submitted_at":"2025-06-10T07:38:57Z","abstract_excerpt":"In this paper, we investigate a resonant system comprising $N$ closely packed spherical resonators ($N>2$). We analyze how the spatial arrangement of these resonators influences the distribution of resonant frequencies, focusing on leading-order terms. Furthermore, we characterize the asymptotic behavior of resonant modes linked to their respective frequencies. Our results demonstrate distinct trends across configurations: For single-row alignment, the system exhibits $N$ clearly separated resonant frequencies; For multi-row arrangements, the resonant frequency range broadens, though the total"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08522","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/2506.08522/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPVUcLb+ddKayZ/vFo0I6sWRYlPG5c/lQul4+Bj3yabk/6bk2Bi9d7OqaJnRGw1XTw9lkdk72+aJSxOdukGrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T20:59:22.140474Z"},"content_sha256":"962e1c1f0cfe065ebb6888ed9b3f99ea2c358e49b9828774650c1bb386a2a612","schema_version":"1.0","event_id":"sha256:962e1c1f0cfe065ebb6888ed9b3f99ea2c358e49b9828774650c1bb386a2a612"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/bundle.json","state_url":"https://pith.science/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/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":"2026-08-08T20:59:22Z","links":{"resolver":"https://pith.science/pith/RWZCE6YFGA47FW6UY7E4VJFTQB","bundle":"https://pith.science/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/bundle.json","state":"https://pith.science/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWZCE6YFGA47FW6UY7E4VJFTQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RWZCE6YFGA47FW6UY7E4VJFTQB","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":"657984570d9523ece8152e49128aec6e4770d85a506b086e97b3eaef0d7046d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-10T07:38:57Z","title_canon_sha256":"76f430285c721ebfe8ff594069242fe73d3d7094663f059fe3e07e749fa9095d"},"schema_version":"1.0","source":{"id":"2506.08522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08522","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08522v1","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08522","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"RWZCE6YFGA47","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_16","alias_value":"RWZCE6YFGA47FW6U","created_at":"2026-07-05T11:18:51Z"},{"alias_kind":"pith_short_8","alias_value":"RWZCE6YF","created_at":"2026-07-05T11:18:51Z"}],"graph_snapshots":[{"event_id":"sha256:962e1c1f0cfe065ebb6888ed9b3f99ea2c358e49b9828774650c1bb386a2a612","target":"graph","created_at":"2026-07-05T11:18:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.08522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate a resonant system comprising $N$ closely packed spherical resonators ($N>2$). We analyze how the spatial arrangement of these resonators influences the distribution of resonant frequencies, focusing on leading-order terms. Furthermore, we characterize the asymptotic behavior of resonant modes linked to their respective frequencies. Our results demonstrate distinct trends across configurations: For single-row alignment, the system exhibits $N$ clearly separated resonant frequencies; For multi-row arrangements, the resonant frequency range broadens, though the total","authors_text":"Haigang Li, Junhua Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-10T07:38:57Z","title":"Resonant frequencies distribution for multiple closely spaced subwavelength resonators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08522","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":"sha256:28f9b6d5f2360b4826db9d257bc40c9767da8ad73da9ca1246d6349d4e9aa132","target":"record","created_at":"2026-07-05T11:18:51Z","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":"657984570d9523ece8152e49128aec6e4770d85a506b086e97b3eaef0d7046d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-10T07:38:57Z","title_canon_sha256":"76f430285c721ebfe8ff594069242fe73d3d7094663f059fe3e07e749fa9095d"},"schema_version":"1.0","source":{"id":"2506.08522","kind":"arxiv","version":1}},"canonical_sha256":"8db2227b053039f2dbd4c7c9caa4b38045890d261a0ac7220a2e0ef5766c1bfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8db2227b053039f2dbd4c7c9caa4b38045890d261a0ac7220a2e0ef5766c1bfe","first_computed_at":"2026-07-05T11:18:51.095383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:51.095383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vqjSI7l8i5T1NQQtUwBda1HLrEHMNS8d7kgw06Kv3G/V+XCuZ0bpWvDMM2jk4DuNXNUyMhDcusEni2DNGrsCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:51.095994Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f9b6d5f2360b4826db9d257bc40c9767da8ad73da9ca1246d6349d4e9aa132","sha256:962e1c1f0cfe065ebb6888ed9b3f99ea2c358e49b9828774650c1bb386a2a612"],"state_sha256":"3988eb658a2d511817fabdddec75638cbf3739ebd025ad7d07bd1d72e431e1a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Eh1xAuZ0rAwbMU/Rx3uJubAyvrbBxCfqExWcLPqrRgLlDgCxPn2nSAYjz6bjA6ErR3LSVG/SBOE4eHcPUbrDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T20:59:22.147453Z","bundle_sha256":"1ec0aa9ac0d762adf062dc1362b379d64aabdf2f37d86838cb91420bcf1e2f6e"}}