{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FANDJDB2IUJE3X7GOGLZLTG746","short_pith_number":"pith:FANDJDB2","canonical_record":{"source":{"id":"1804.07752","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-20T17:54:30Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"title_canon_sha256":"9958a3c00a8ad03f6770aa60941793375e7fdd93e65dda3835d55aff8dbf6d66","abstract_canon_sha256":"c984c5dcc11239a3090a749bf61a1a8b1a29a721f461120d93cb01970d138f33"},"schema_version":"1.0"},"canonical_sha256":"281a348c3a45124ddfe6719795ccdfe7be30c21ecd6f1f656bbc4d75a65df2e5","source":{"kind":"arxiv","id":"1804.07752","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07752","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07752v5","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07752","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"FANDJDB2IUJE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FANDJDB2IUJE3X7G","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FANDJDB2","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FANDJDB2IUJE3X7GOGLZLTG746","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07752","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-20T17:54:30Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"title_canon_sha256":"9958a3c00a8ad03f6770aa60941793375e7fdd93e65dda3835d55aff8dbf6d66","abstract_canon_sha256":"c984c5dcc11239a3090a749bf61a1a8b1a29a721f461120d93cb01970d138f33"},"schema_version":"1.0"},"canonical_sha256":"281a348c3a45124ddfe6719795ccdfe7be30c21ecd6f1f656bbc4d75a65df2e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:41.653130Z","signature_b64":"ITaqKbpZqaiErbrEtkoRMINOlkG7R4VsAKuvvEW7SEDOGfoxDbJk1vPv9C0N4WH7EpIGebF1cMeOM0Xn7GqhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"281a348c3a45124ddfe6719795ccdfe7be30c21ecd6f1f656bbc4d75a65df2e5","last_reissued_at":"2026-05-17T23:58:41.652494Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:41.652494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07752","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7p2kXOBrcx/Z05aGeoToD3hUy2JcgZ777jFrfHm2TMZYN1inFclVU8eXP/+uXsoGwMiQLyX+GpUXu4Av5n9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:20:59.385604Z"},"content_sha256":"a1f86a7d42a3d458790abeaf5846a2311b6f1e7ee8e496b201c97c5efb7c6c15","schema_version":"1.0","event_id":"sha256:a1f86a7d42a3d458790abeaf5846a2311b6f1e7ee8e496b201c97c5efb7c6c15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FANDJDB2IUJE3X7GOGLZLTG746","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dyson equation with linear self-energy: spectral bands, edges and cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Johannes Alt, Laszlo Erdos, Torben Kr\\\"uger","submitted_at":"2018-04-20T17:54:30Z","abstract_excerpt":"We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a + S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint $\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is a self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving linear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform of a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under suitable assumptions, we establish that this measure has a uniformly $1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07752","kind":"arxiv","version":5},"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":"2026-05-17T23:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KfqixMJLBFjqQL6p2Bbvc/pRNYHsAeiEJ6Vb9NCoYa5ohBlk773ASgg6pszUeUpckDGuC8mrGZRzPrZ5VhhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:20:59.386232Z"},"content_sha256":"cb65366a31b9dade022d1ae1639292f1fb16cd97414e443980f36d0edc612a33","schema_version":"1.0","event_id":"sha256:cb65366a31b9dade022d1ae1639292f1fb16cd97414e443980f36d0edc612a33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FANDJDB2IUJE3X7GOGLZLTG746/bundle.json","state_url":"https://pith.science/pith/FANDJDB2IUJE3X7GOGLZLTG746/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FANDJDB2IUJE3X7GOGLZLTG746/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":"2026-05-27T15:20:59Z","links":{"resolver":"https://pith.science/pith/FANDJDB2IUJE3X7GOGLZLTG746","bundle":"https://pith.science/pith/FANDJDB2IUJE3X7GOGLZLTG746/bundle.json","state":"https://pith.science/pith/FANDJDB2IUJE3X7GOGLZLTG746/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FANDJDB2IUJE3X7GOGLZLTG746/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FANDJDB2IUJE3X7GOGLZLTG746","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":"c984c5dcc11239a3090a749bf61a1a8b1a29a721f461120d93cb01970d138f33","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-20T17:54:30Z","title_canon_sha256":"9958a3c00a8ad03f6770aa60941793375e7fdd93e65dda3835d55aff8dbf6d66"},"schema_version":"1.0","source":{"id":"1804.07752","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07752","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07752v5","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07752","created_at":"2026-05-17T23:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"FANDJDB2IUJE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FANDJDB2IUJE3X7G","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FANDJDB2","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:cb65366a31b9dade022d1ae1639292f1fb16cd97414e443980f36d0edc612a33","target":"graph","created_at":"2026-05-17T23:58:41Z","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 study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a + S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint $\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is a self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving linear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform of a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under suitable assumptions, we establish that this measure has a uniformly $1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure,","authors_text":"Johannes Alt, Laszlo Erdos, Torben Kr\\\"uger","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-20T17:54:30Z","title":"The Dyson equation with linear self-energy: spectral bands, edges and cusps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07752","kind":"arxiv","version":5},"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:a1f86a7d42a3d458790abeaf5846a2311b6f1e7ee8e496b201c97c5efb7c6c15","target":"record","created_at":"2026-05-17T23:58:41Z","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":"c984c5dcc11239a3090a749bf61a1a8b1a29a721f461120d93cb01970d138f33","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-20T17:54:30Z","title_canon_sha256":"9958a3c00a8ad03f6770aa60941793375e7fdd93e65dda3835d55aff8dbf6d66"},"schema_version":"1.0","source":{"id":"1804.07752","kind":"arxiv","version":5}},"canonical_sha256":"281a348c3a45124ddfe6719795ccdfe7be30c21ecd6f1f656bbc4d75a65df2e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"281a348c3a45124ddfe6719795ccdfe7be30c21ecd6f1f656bbc4d75a65df2e5","first_computed_at":"2026-05-17T23:58:41.652494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:41.652494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ITaqKbpZqaiErbrEtkoRMINOlkG7R4VsAKuvvEW7SEDOGfoxDbJk1vPv9C0N4WH7EpIGebF1cMeOM0Xn7GqhDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:41.653130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07752","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1f86a7d42a3d458790abeaf5846a2311b6f1e7ee8e496b201c97c5efb7c6c15","sha256:cb65366a31b9dade022d1ae1639292f1fb16cd97414e443980f36d0edc612a33"],"state_sha256":"db0f4744edb8c503f8b3da4e1073f659cf60e552d8cd82d10bc493484da3553b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nmPVI102sTwRA5lRxsdDYEqc/D1HtfsywTkNLIZK/nTZx3q43hLxJnnn4NHM3lBSQVp0w8XU1pnA5gKUhhzCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:20:59.389351Z","bundle_sha256":"175f71814e59ed628e56633da8c2d5e724862723fc3ba0753c440a368a3e0de9"}}