{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NAHHRL7PZ6MCH6XVSSNA2UVKGL","short_pith_number":"pith:NAHHRL7P","canonical_record":{"source":{"id":"1209.5641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-25T15:23:49Z","cross_cats_sorted":["hep-ph","quant-ph"],"title_canon_sha256":"f76ccb4dafa68e826ce9d31530fd865887d5a8402cd4c3ee69f2ffe0e6796271","abstract_canon_sha256":"3bee45e04f62e0107645fc0373431c59002f35dabea1013412c56943c12a05ff"},"schema_version":"1.0"},"canonical_sha256":"680e78afefcf9823faf5949a0d52aa32f0bf79b54a71ae75ef3ad92d2a566632","source":{"kind":"arxiv","id":"1209.5641","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5641","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5641v2","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5641","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"pith_short_12","alias_value":"NAHHRL7PZ6MC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NAHHRL7PZ6MCH6XV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NAHHRL7P","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NAHHRL7PZ6MCH6XVSSNA2UVKGL","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-25T15:23:49Z","cross_cats_sorted":["hep-ph","quant-ph"],"title_canon_sha256":"f76ccb4dafa68e826ce9d31530fd865887d5a8402cd4c3ee69f2ffe0e6796271","abstract_canon_sha256":"3bee45e04f62e0107645fc0373431c59002f35dabea1013412c56943c12a05ff"},"schema_version":"1.0"},"canonical_sha256":"680e78afefcf9823faf5949a0d52aa32f0bf79b54a71ae75ef3ad92d2a566632","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:16.030063Z","signature_b64":"O2VK2r7HGTLwKDuMAOd6PLfEQNECkeA5WOFldKyk+tKIc4iw9dfOd/62zoOKL3OZf8Nxqmm0pq7G8EyI2a7JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"680e78afefcf9823faf5949a0d52aa32f0bf79b54a71ae75ef3ad92d2a566632","last_reissued_at":"2026-05-18T03:34:16.029292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:16.029292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5641","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":"2026-05-18T03:34:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lyd+og/kJw7ieLWnlf0fJOREStZt+CVG4wgwROj/S8/im6rvNFK2zToqHgnIPac5DbvZ2mhFWIgffp5znJh8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:05:10.704121Z"},"content_sha256":"30a479f0b48bce5412f2576393b90395c6e226c1019b401fd42f423161d4fd07","schema_version":"1.0","event_id":"sha256:30a479f0b48bce5412f2576393b90395c6e226c1019b401fd42f423161d4fd07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NAHHRL7PZ6MCH6XVSSNA2UVKGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","quant-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Christof Wetterich, Igor Boettcher, Jan M. Pawlowski, Sebastian Diehl","submitted_at":"2012-09-25T15:23:49Z","abstract_excerpt":"We derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, chemical potential and Fermi momentum. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger-Dyson equation for the fermion propagator, and compute the perturbative contact on the BCS and BEC sides within this framework. A Functional Renormalization Group approach is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5641","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":"2026-05-18T03:34:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRN9TGNecfmj199KwrjTYk/BQ3IifzD8kvmwmSYbIQ44HYm6Q2qp8YJoPlcjRCo1wGpmV1clx00qqZJ496BGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:05:10.704731Z"},"content_sha256":"2681443f05771e0cfd3e548f8c21a1b9986e3ad57711263b907a4af00d3ea523","schema_version":"1.0","event_id":"sha256:2681443f05771e0cfd3e548f8c21a1b9986e3ad57711263b907a4af00d3ea523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/bundle.json","state_url":"https://pith.science/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/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":"2026-05-27T14:05:10Z","links":{"resolver":"https://pith.science/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL","bundle":"https://pith.science/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/bundle.json","state":"https://pith.science/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NAHHRL7PZ6MCH6XVSSNA2UVKGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NAHHRL7PZ6MCH6XVSSNA2UVKGL","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":"3bee45e04f62e0107645fc0373431c59002f35dabea1013412c56943c12a05ff","cross_cats_sorted":["hep-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-25T15:23:49Z","title_canon_sha256":"f76ccb4dafa68e826ce9d31530fd865887d5a8402cd4c3ee69f2ffe0e6796271"},"schema_version":"1.0","source":{"id":"1209.5641","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5641","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5641v2","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5641","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"pith_short_12","alias_value":"NAHHRL7PZ6MC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NAHHRL7PZ6MCH6XV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NAHHRL7P","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:2681443f05771e0cfd3e548f8c21a1b9986e3ad57711263b907a4af00d3ea523","target":"graph","created_at":"2026-05-18T03:34:16Z","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 derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, chemical potential and Fermi momentum. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger-Dyson equation for the fermion propagator, and compute the perturbative contact on the BCS and BEC sides within this framework. A Functional Renormalization Group approach is ","authors_text":"Christof Wetterich, Igor Boettcher, Jan M. Pawlowski, Sebastian Diehl","cross_cats":["hep-ph","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-25T15:23:49Z","title":"Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5641","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":"sha256:30a479f0b48bce5412f2576393b90395c6e226c1019b401fd42f423161d4fd07","target":"record","created_at":"2026-05-18T03:34:16Z","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":"3bee45e04f62e0107645fc0373431c59002f35dabea1013412c56943c12a05ff","cross_cats_sorted":["hep-ph","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2012-09-25T15:23:49Z","title_canon_sha256":"f76ccb4dafa68e826ce9d31530fd865887d5a8402cd4c3ee69f2ffe0e6796271"},"schema_version":"1.0","source":{"id":"1209.5641","kind":"arxiv","version":2}},"canonical_sha256":"680e78afefcf9823faf5949a0d52aa32f0bf79b54a71ae75ef3ad92d2a566632","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"680e78afefcf9823faf5949a0d52aa32f0bf79b54a71ae75ef3ad92d2a566632","first_computed_at":"2026-05-18T03:34:16.029292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:16.029292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2VK2r7HGTLwKDuMAOd6PLfEQNECkeA5WOFldKyk+tKIc4iw9dfOd/62zoOKL3OZf8Nxqmm0pq7G8EyI2a7JDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:16.030063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5641","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a479f0b48bce5412f2576393b90395c6e226c1019b401fd42f423161d4fd07","sha256:2681443f05771e0cfd3e548f8c21a1b9986e3ad57711263b907a4af00d3ea523"],"state_sha256":"8a8fc427c02c6bdc0eb5ab4050cb56a44e512659fd6c3615188eb62440780dc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2A5SvdASvB1VuGNDl9gFk07CUR5zRnsF7Do1i9j+Tw2C5uHaMBh13UpdX56k7q+QaZDDRVJwdC40HVpi3tA9DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:05:10.708070Z","bundle_sha256":"9422118a137af4a7734eb6d3edc30f11741c5b322e09a85a6b5a92d071ccecb6"}}