{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AADBEWYVWX3QE7PTVBC46KGMKP","short_pith_number":"pith:AADBEWYV","canonical_record":{"source":{"id":"2607.02557","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2026-06-27T21:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"4c28676dae77620bd2f227d17ded41019f20131bf42c2f7e9622f5fb593ae9d2","abstract_canon_sha256":"a2ad4778c22880c80ffb07d5730eb1b1dce5cae029d7bf70599cedfa2ea377c0"},"schema_version":"1.0"},"canonical_sha256":"0006125b15b5f7027df3a845cf28cc53c5a30c716ad7dacaf0915a596387853d","source":{"kind":"arxiv","id":"2607.02557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02557","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02557v1","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02557","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"AADBEWYVWX3Q","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_16","alias_value":"AADBEWYVWX3QE7PT","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_8","alias_value":"AADBEWYV","created_at":"2026-07-07T00:16:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AADBEWYVWX3QE7PTVBC46KGMKP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.02557","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2026-06-27T21:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"4c28676dae77620bd2f227d17ded41019f20131bf42c2f7e9622f5fb593ae9d2","abstract_canon_sha256":"a2ad4778c22880c80ffb07d5730eb1b1dce5cae029d7bf70599cedfa2ea377c0"},"schema_version":"1.0"},"canonical_sha256":"0006125b15b5f7027df3a845cf28cc53c5a30c716ad7dacaf0915a596387853d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T00:16:00.480907Z","signature_b64":"SUsPX90+PvexgYOg6ZiHDrI4UDrHM+W2SFXL8MQLFPEBKmRQ2I9uLAZc0GO51wbXwI1/uERXKjWXe8rn/6ujBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0006125b15b5f7027df3a845cf28cc53c5a30c716ad7dacaf0915a596387853d","last_reissued_at":"2026-07-07T00:16:00.480042Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T00:16:00.480042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.02557","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":"2026-07-07T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjrVPYXzrOE198a8lTBYkry5mu1dRyUEcK8vRgY9qHxNicTXH9NcqubpXswFvQ6achWhVGbCvgk3e2VwSR4NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:59:59.695785Z"},"content_sha256":"b3601bbaf0770c66d391edf6f86b23b2f3c260eb73d0bc33aa4d4fb4692b71fa","schema_version":"1.0","event_id":"sha256:b3601bbaf0770c66d391edf6f86b23b2f3c260eb73d0bc33aa4d4fb4692b71fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AADBEWYVWX3QE7PTVBC46KGMKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synthesis of passive multidimensional scattering matrices: a survey","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Sankar Basu (National Science Foundation, USA)","submitted_at":"2026-06-27T21:21:41Z","abstract_excerpt":"The goal of this exposition is twofold. First, it surveys the current status of the synthesis of rational multivariable ($n$-dimensional) passive linear shift-invariant bounded-real (or positive-real) transfer functions as scattering (or immittance) matrices of networks composed of a finite number of $n$ types of inductive and capacitive elements together with memoryless reciprocal and nonreciprocal components, such as transformers and gyrators. The theory seeks to extend the classical $1$-D network synthesis framework to the multidimensional ($n$-D) setting. Second, the exposition examines th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02557","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/2607.02557/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":"2026-07-07T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4MkXRnVDCtUvkrHng5uDkJRgbF0AEDyj7JRc7C6PoPZPFonoc12ZHSLSqPpzWifJqkmWFFQihB+X8xe7UOupAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:59:59.696318Z"},"content_sha256":"d77ff9a8b4ce00bd496a9c6d1d7281f876b9a57b66c238a996274b03f344419a","schema_version":"1.0","event_id":"sha256:d77ff9a8b4ce00bd496a9c6d1d7281f876b9a57b66c238a996274b03f344419a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AADBEWYVWX3QE7PTVBC46KGMKP/bundle.json","state_url":"https://pith.science/pith/AADBEWYVWX3QE7PTVBC46KGMKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AADBEWYVWX3QE7PTVBC46KGMKP/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":"2026-08-12T08:59:59Z","links":{"resolver":"https://pith.science/pith/AADBEWYVWX3QE7PTVBC46KGMKP","bundle":"https://pith.science/pith/AADBEWYVWX3QE7PTVBC46KGMKP/bundle.json","state":"https://pith.science/pith/AADBEWYVWX3QE7PTVBC46KGMKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AADBEWYVWX3QE7PTVBC46KGMKP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AADBEWYVWX3QE7PTVBC46KGMKP","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":"a2ad4778c22880c80ffb07d5730eb1b1dce5cae029d7bf70599cedfa2ea377c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2026-06-27T21:21:41Z","title_canon_sha256":"4c28676dae77620bd2f227d17ded41019f20131bf42c2f7e9622f5fb593ae9d2"},"schema_version":"1.0","source":{"id":"2607.02557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02557","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02557v1","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02557","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"AADBEWYVWX3Q","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_16","alias_value":"AADBEWYVWX3QE7PT","created_at":"2026-07-07T00:16:00Z"},{"alias_kind":"pith_short_8","alias_value":"AADBEWYV","created_at":"2026-07-07T00:16:00Z"}],"graph_snapshots":[{"event_id":"sha256:d77ff9a8b4ce00bd496a9c6d1d7281f876b9a57b66c238a996274b03f344419a","target":"graph","created_at":"2026-07-07T00:16:00Z","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/2607.02557/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of this exposition is twofold. First, it surveys the current status of the synthesis of rational multivariable ($n$-dimensional) passive linear shift-invariant bounded-real (or positive-real) transfer functions as scattering (or immittance) matrices of networks composed of a finite number of $n$ types of inductive and capacitive elements together with memoryless reciprocal and nonreciprocal components, such as transformers and gyrators. The theory seeks to extend the classical $1$-D network synthesis framework to the multidimensional ($n$-D) setting. Second, the exposition examines th","authors_text":"Sankar Basu (National Science Foundation, USA)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2026-06-27T21:21:41Z","title":"Synthesis of passive multidimensional scattering matrices: a survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02557","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:b3601bbaf0770c66d391edf6f86b23b2f3c260eb73d0bc33aa4d4fb4692b71fa","target":"record","created_at":"2026-07-07T00:16:00Z","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":"a2ad4778c22880c80ffb07d5730eb1b1dce5cae029d7bf70599cedfa2ea377c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SP","submitted_at":"2026-06-27T21:21:41Z","title_canon_sha256":"4c28676dae77620bd2f227d17ded41019f20131bf42c2f7e9622f5fb593ae9d2"},"schema_version":"1.0","source":{"id":"2607.02557","kind":"arxiv","version":1}},"canonical_sha256":"0006125b15b5f7027df3a845cf28cc53c5a30c716ad7dacaf0915a596387853d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0006125b15b5f7027df3a845cf28cc53c5a30c716ad7dacaf0915a596387853d","first_computed_at":"2026-07-07T00:16:00.480042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T00:16:00.480042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUsPX90+PvexgYOg6ZiHDrI4UDrHM+W2SFXL8MQLFPEBKmRQ2I9uLAZc0GO51wbXwI1/uERXKjWXe8rn/6ujBQ==","signature_status":"signed_v1","signed_at":"2026-07-07T00:16:00.480907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3601bbaf0770c66d391edf6f86b23b2f3c260eb73d0bc33aa4d4fb4692b71fa","sha256:d77ff9a8b4ce00bd496a9c6d1d7281f876b9a57b66c238a996274b03f344419a"],"state_sha256":"beeeddea00c74b75da011d154dcd924a6169d690556515b3ad11dcb528338691"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p10qtbVSidE6sC5Z/mAR4lqsK78xu7RlLeH1ty9CgUdaCDbZkVKW8KDEMKpJuliCSavV4VMJPKBDgKLvscPBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T08:59:59.701843Z","bundle_sha256":"9de048a1c9cd6185e20d1645711c163985c1d26a15e076fd4b496f41778b6a57"}}