{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3ZKV3TGRMJED5VEXUOKOUIWNOR","short_pith_number":"pith:3ZKV3TGR","canonical_record":{"source":{"id":"1703.04616","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-14T17:42:24Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"title_canon_sha256":"c80a9418b84e9086a47ad6a1c264d93c68cc81e1f4917f918e107c60cef5edf3","abstract_canon_sha256":"544c581a3e64fbe881f62b60cdaa0a725e14e192f5087f4bd848ff495fe8a173"},"schema_version":"1.0"},"canonical_sha256":"de555dccd162483ed497a394ea22cd7450e524b2f2c173f04f22443799421890","source":{"kind":"arxiv","id":"1703.04616","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04616","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04616v2","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04616","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"3ZKV3TGRMJED","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZKV3TGRMJED5VEX","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZKV3TGR","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3ZKV3TGRMJED5VEXUOKOUIWNOR","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04616","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-14T17:42:24Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"title_canon_sha256":"c80a9418b84e9086a47ad6a1c264d93c68cc81e1f4917f918e107c60cef5edf3","abstract_canon_sha256":"544c581a3e64fbe881f62b60cdaa0a725e14e192f5087f4bd848ff495fe8a173"},"schema_version":"1.0"},"canonical_sha256":"de555dccd162483ed497a394ea22cd7450e524b2f2c173f04f22443799421890","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:46.145194Z","signature_b64":"7/DjhtBK+tXg5yecVd8C/6k1S8HvyCIJ58X8WqDnCWy22/8+8q8yh1TtMaU8ipA+y1uPSo2MH2Qb836qXvZQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de555dccd162483ed497a394ea22cd7450e524b2f2c173f04f22443799421890","last_reissued_at":"2026-05-18T00:38:46.144642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:46.144642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04616","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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8qcFVhcXtkLkKbWUKy67wW8i5XrAt1p1fBowFAdkyEYDxlHPg8PbIP40PkTj21NXzt+yP/mpDtdiZTim257BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:50:31.694099Z"},"content_sha256":"091d913ff6d5171bf847cc714b20f7dfffcc5278513e0b7b0a4ed47c3e7a22a6","schema_version":"1.0","event_id":"sha256:091d913ff6d5171bf847cc714b20f7dfffcc5278513e0b7b0a4ed47c3e7a22a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3ZKV3TGRMJED5VEXUOKOUIWNOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound for the BCS functional with boundary conditions at infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andreas Deuchert","submitted_at":"2017-03-14T17:42:24Z","abstract_excerpt":"We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of BCS theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04616","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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KT7LY73+BFcoH0OtAADbUBMErlSFOHxvhleiJDSrNVFc3L8isxIR8YSM75LTd1dDFDyqdunXEJWqTHrgs32ZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:50:31.694464Z"},"content_sha256":"a20edbb9b088d60ff0add8213b2c61e3cd906a29f98cbed698ce400f402d5d8f","schema_version":"1.0","event_id":"sha256:a20edbb9b088d60ff0add8213b2c61e3cd906a29f98cbed698ce400f402d5d8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/bundle.json","state_url":"https://pith.science/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/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":"2026-06-02T07:50:31Z","links":{"resolver":"https://pith.science/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR","bundle":"https://pith.science/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/bundle.json","state":"https://pith.science/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ZKV3TGRMJED5VEXUOKOUIWNOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ZKV3TGRMJED5VEXUOKOUIWNOR","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":"544c581a3e64fbe881f62b60cdaa0a725e14e192f5087f4bd848ff495fe8a173","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-14T17:42:24Z","title_canon_sha256":"c80a9418b84e9086a47ad6a1c264d93c68cc81e1f4917f918e107c60cef5edf3"},"schema_version":"1.0","source":{"id":"1703.04616","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04616","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04616v2","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04616","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"3ZKV3TGRMJED","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3ZKV3TGRMJED5VEX","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3ZKV3TGR","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:a20edbb9b088d60ff0add8213b2c61e3cd906a29f98cbed698ce400f402d5d8f","target":"graph","created_at":"2026-05-18T00:38:46Z","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":"We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of BCS theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.","authors_text":"Andreas Deuchert","cross_cats":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-14T17:42:24Z","title":"A lower bound for the BCS functional with boundary conditions at infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04616","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":"sha256:091d913ff6d5171bf847cc714b20f7dfffcc5278513e0b7b0a4ed47c3e7a22a6","target":"record","created_at":"2026-05-18T00:38:46Z","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":"544c581a3e64fbe881f62b60cdaa0a725e14e192f5087f4bd848ff495fe8a173","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.supr-con","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-14T17:42:24Z","title_canon_sha256":"c80a9418b84e9086a47ad6a1c264d93c68cc81e1f4917f918e107c60cef5edf3"},"schema_version":"1.0","source":{"id":"1703.04616","kind":"arxiv","version":2}},"canonical_sha256":"de555dccd162483ed497a394ea22cd7450e524b2f2c173f04f22443799421890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de555dccd162483ed497a394ea22cd7450e524b2f2c173f04f22443799421890","first_computed_at":"2026-05-18T00:38:46.144642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:46.144642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/DjhtBK+tXg5yecVd8C/6k1S8HvyCIJ58X8WqDnCWy22/8+8q8yh1TtMaU8ipA+y1uPSo2MH2Qb836qXvZQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:46.145194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04616","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091d913ff6d5171bf847cc714b20f7dfffcc5278513e0b7b0a4ed47c3e7a22a6","sha256:a20edbb9b088d60ff0add8213b2c61e3cd906a29f98cbed698ce400f402d5d8f"],"state_sha256":"f1dcb0c50c30866c9bdb6e2eb1d910c45c476e9b90d6099c7be22924e87cfad8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQYTrIhdn782/xW5hHd/j9gx4Qf6b/jcmHP8irelIG2MRkuKP5ipRVoWwzUsE0C0byyRqGwM/SNxNlbDx20TCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:50:31.696465Z","bundle_sha256":"89b3950234a060a38eac1d04e43b0b4727c09bd794acfea637d2c27b0b284d56"}}