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We solve this relative initial-state problem for normalized polynomial filters, $\\ket{\\psi_Q}=Q(H)\\ket{K_0}/\\sqrt{N_Q}$ with $N_Q=\\langle K_0|Q(H)^\\dagger Q(H)|K_0\\rangle$. The filtered spectral measure is the positive polynomial modification $|Q(E)|^2\\mathrm d\\mu(E)/N_Q$, and orthogonality turns this measure change into a finite-band transfer from reference Fourie"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.05294","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-06T16:37:39Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"697477d8d4afa63646ee0ed222d84da1377c9aca5d8af151cae2dd09e025a376","abstract_canon_sha256":"8e64f88cb336938f62757a40965c6322f74def7b3565c77e3e405800237f1f8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T03:19:22.503263Z","signature_b64":"2aJfiyBMluGRZz3UML6nUvsqlRkKFVeymK+mYHX2lOP1bO+zBnja1oLmKP5d68iP635zL6A8zpeZ0ajUhw9GDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a963ca613896ee5c52c28d91b7aebb3c01e9dc24b465c3de67f7a12aad068229","last_reissued_at":"2026-07-07T03:19:22.502745Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T03:19:22.502745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Abhishek Chowdhury, Ajit Prasad Mahapatra","submitted_at":"2026-07-06T16:37:39Z","abstract_excerpt":"State Krylov, or spread, complexity is a property of a pair $(H,\\ket{K_0})$ rather than of the Hamiltonian alone. 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The filtered spectral measure is the positive polynomial modification $|Q(E)|^2\\mathrm d\\mu(E)/N_Q$, and orthogonality turns this measure change into a finite-band transfer from reference Fourie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05294","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/2607.05294/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.05294","created_at":"2026-07-07T03:19:22.502828+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.05294v1","created_at":"2026-07-07T03:19:22.502828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05294","created_at":"2026-07-07T03:19:22.502828+00:00"},{"alias_kind":"pith_short_12","alias_value":"VFR4UYJYS3XF","created_at":"2026-07-07T03:19:22.502828+00:00"},{"alias_kind":"pith_short_16","alias_value":"VFR4UYJYS3XFYUWC","created_at":"2026-07-07T03:19:22.502828+00:00"},{"alias_kind":"pith_short_8","alias_value":"VFR4UYJY","created_at":"2026-07-07T03:19:22.502828+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.10072","citing_title":"Recursion Coefficients and Krylov Dynamics in Polynomial Random Matrix Models","ref_index":78,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ","json":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ.json","graph_json":"https://pith.science/api/pith-number/VFR4UYJYS3XFYUWCRWI3PLV3HQ/graph.json","events_json":"https://pith.science/api/pith-number/VFR4UYJYS3XFYUWCRWI3PLV3HQ/events.json","paper":"https://pith.science/paper/VFR4UYJY"},"agent_actions":{"view_html":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ","download_json":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ.json","view_paper":"https://pith.science/paper/VFR4UYJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.05294&json=true","fetch_graph":"https://pith.science/api/pith-number/VFR4UYJYS3XFYUWCRWI3PLV3HQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VFR4UYJYS3XFYUWCRWI3PLV3HQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ/action/storage_attestation","attest_author":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ/action/author_attestation","sign_citation":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ/action/citation_signature","submit_replication":"https://pith.science/pith/VFR4UYJYS3XFYUWCRWI3PLV3HQ/action/replication_record"}},"created_at":"2026-07-07T03:19:22.502828+00:00","updated_at":"2026-07-07T03:19:22.502828+00:00"}