{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MQE5EZJUHYSNCEHCQJ3VAZ255V","short_pith_number":"pith:MQE5EZJU","canonical_record":{"source":{"id":"2607.03937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2026-07-04T16:12:40Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"033493fa4a299e828ed5259bfb565955907fa474d639a68706b3c1a25d17252b","abstract_canon_sha256":"73350ead172225f1251d058c38ec6d997feeba03b58bf13fcb74a5487478e936"},"schema_version":"1.0"},"canonical_sha256":"6409d265343e24d110e2827750675ded595cadf3ddc5d0f874d969c74e454c21","source":{"kind":"arxiv","id":"2607.03937","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03937","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03937v1","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03937","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"MQE5EZJUHYSN","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"MQE5EZJUHYSNCEHC","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"MQE5EZJU","created_at":"2026-07-07T02:18:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MQE5EZJUHYSNCEHCQJ3VAZ255V","target":"record","payload":{"canonical_record":{"source":{"id":"2607.03937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2026-07-04T16:12:40Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"033493fa4a299e828ed5259bfb565955907fa474d639a68706b3c1a25d17252b","abstract_canon_sha256":"73350ead172225f1251d058c38ec6d997feeba03b58bf13fcb74a5487478e936"},"schema_version":"1.0"},"canonical_sha256":"6409d265343e24d110e2827750675ded595cadf3ddc5d0f874d969c74e454c21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:15.572622Z","signature_b64":"RQx7HUbUJ7TCQSqIOEO7C9Z0udbZIO/mFkJcv4zd2nJ8fN54vWBZ51rzlvzoOiT4zz0WhzrqOQyf0ttEZT+QCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6409d265343e24d110e2827750675ded595cadf3ddc5d0f874d969c74e454c21","last_reissued_at":"2026-07-07T02:18:15.571810Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:15.571810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.03937","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":"2026-07-07T02:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXjSOXb0WhVVYJB9JURhfZInPddaYxRGIsOy5byBpz/hja8TtufaTZTMul9+pw/BRQ7EeFaBJjUmTUl1KgHdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:45:28.289704Z"},"content_sha256":"8c7f4c90e84cfbe7842a971d53a837e25208aa7b18dd58b5fe9403dfec4a686c","schema_version":"1.0","event_id":"sha256:8c7f4c90e84cfbe7842a971d53a837e25208aa7b18dd58b5fe9403dfec4a686c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MQE5EZJUHYSNCEHCQJ3VAZ255V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evidence of the Cooper-Pair Field with Gaussian Memory Kernel in Unconventional Superconductors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.supr-con","authors_text":"Udomsilp Pinsook","submitted_at":"2026-07-04T16:12:40Z","abstract_excerpt":"We develop a dynamical description of the superconducting pair field in which the Cooper-channel Hubbard--Stratonovich field $\\Delta$ is treated as a memory-dressed Bogoliubov pair field rather than as a purely static order parameter. Starting from the standard pair-field effective action, we couple $\\Delta$ to antinode-selected collective or self-generated fields. An ensemble of such modes produces a distribution of local Bogoliubov frequencies; when this distribution is approximately Gaussian, ensemble averaging gives the memory factor $\\exp[-t^2/(2\\tau_g^2)]$. In cuprate superconductors, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03937","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/2607.03937/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":"2026-07-07T02:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v0DeAdUW6qTIxwixxMDOX3t7VUnoVN5Elc6ovScOIIk0sWmXdB14TQisJPWXLVCeUSCjzFJ7rm7ps6aDoKikBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:45:28.290635Z"},"content_sha256":"e0799267afc41e140fafc516f8d9e6fe60ceccd7d99ff858522f1d5be21648e1","schema_version":"1.0","event_id":"sha256:e0799267afc41e140fafc516f8d9e6fe60ceccd7d99ff858522f1d5be21648e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/bundle.json","state_url":"https://pith.science/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/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":"2026-08-09T19:45:28Z","links":{"resolver":"https://pith.science/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V","bundle":"https://pith.science/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/bundle.json","state":"https://pith.science/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQE5EZJUHYSNCEHCQJ3VAZ255V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MQE5EZJUHYSNCEHCQJ3VAZ255V","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":"73350ead172225f1251d058c38ec6d997feeba03b58bf13fcb74a5487478e936","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2026-07-04T16:12:40Z","title_canon_sha256":"033493fa4a299e828ed5259bfb565955907fa474d639a68706b3c1a25d17252b"},"schema_version":"1.0","source":{"id":"2607.03937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03937","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03937v1","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03937","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"MQE5EZJUHYSN","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_16","alias_value":"MQE5EZJUHYSNCEHC","created_at":"2026-07-07T02:18:15Z"},{"alias_kind":"pith_short_8","alias_value":"MQE5EZJU","created_at":"2026-07-07T02:18:15Z"}],"graph_snapshots":[{"event_id":"sha256:e0799267afc41e140fafc516f8d9e6fe60ceccd7d99ff858522f1d5be21648e1","target":"graph","created_at":"2026-07-07T02:18:15Z","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/2607.03937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a dynamical description of the superconducting pair field in which the Cooper-channel Hubbard--Stratonovich field $\\Delta$ is treated as a memory-dressed Bogoliubov pair field rather than as a purely static order parameter. Starting from the standard pair-field effective action, we couple $\\Delta$ to antinode-selected collective or self-generated fields. An ensemble of such modes produces a distribution of local Bogoliubov frequencies; when this distribution is approximately Gaussian, ensemble averaging gives the memory factor $\\exp[-t^2/(2\\tau_g^2)]$. In cuprate superconductors, th","authors_text":"Udomsilp Pinsook","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2026-07-04T16:12:40Z","title":"Evidence of the Cooper-Pair Field with Gaussian Memory Kernel in Unconventional Superconductors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03937","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":"sha256:8c7f4c90e84cfbe7842a971d53a837e25208aa7b18dd58b5fe9403dfec4a686c","target":"record","created_at":"2026-07-07T02:18:15Z","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":"73350ead172225f1251d058c38ec6d997feeba03b58bf13fcb74a5487478e936","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2026-07-04T16:12:40Z","title_canon_sha256":"033493fa4a299e828ed5259bfb565955907fa474d639a68706b3c1a25d17252b"},"schema_version":"1.0","source":{"id":"2607.03937","kind":"arxiv","version":1}},"canonical_sha256":"6409d265343e24d110e2827750675ded595cadf3ddc5d0f874d969c74e454c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6409d265343e24d110e2827750675ded595cadf3ddc5d0f874d969c74e454c21","first_computed_at":"2026-07-07T02:18:15.571810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:18:15.571810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQx7HUbUJ7TCQSqIOEO7C9Z0udbZIO/mFkJcv4zd2nJ8fN54vWBZ51rzlvzoOiT4zz0WhzrqOQyf0ttEZT+QCw==","signature_status":"signed_v1","signed_at":"2026-07-07T02:18:15.572622Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c7f4c90e84cfbe7842a971d53a837e25208aa7b18dd58b5fe9403dfec4a686c","sha256:e0799267afc41e140fafc516f8d9e6fe60ceccd7d99ff858522f1d5be21648e1"],"state_sha256":"37b8ddf3ad30c3fd1a2e0bee73a4a1146b1db8656d7e1d4f6abdbb5f1c519af7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Brmyddw5ncD41gb2zoYF9OxsGW17Y7pxsC7sTcOIV9MuavggGmOBmbNzbUNHC2DlviwoxsSzrppe+MRscxcCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:45:28.296102Z","bundle_sha256":"70e619cb06e99eed88b51fc411a3fe698b96d6b5c9153c2ba911e4fffa6220c3"}}