{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QZNWYYL4634AVMRD7SQ6XYVQV5","short_pith_number":"pith:QZNWYYL4","canonical_record":{"source":{"id":"2607.23240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-25T14:53:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bd502523e1b4089e48a07eea108bfdea91c19b4c1c705dfb55215913871bff71","abstract_canon_sha256":"d6619ed4158cbbe6e2825372e5e96f90d04672dac1c27db2f13da1b264521a27"},"schema_version":"1.0"},"canonical_sha256":"865b6c617cf6f80ab223fca1ebe2b0af68fd86108560ffae201322df769d2903","source":{"kind":"arxiv","id":"2607.23240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23240","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23240v1","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23240","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_12","alias_value":"QZNWYYL4634A","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_16","alias_value":"QZNWYYL4634AVMRD","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_8","alias_value":"QZNWYYL4","created_at":"2026-07-28T01:22:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QZNWYYL4634AVMRD7SQ6XYVQV5","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-25T14:53:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bd502523e1b4089e48a07eea108bfdea91c19b4c1c705dfb55215913871bff71","abstract_canon_sha256":"d6619ed4158cbbe6e2825372e5e96f90d04672dac1c27db2f13da1b264521a27"},"schema_version":"1.0"},"canonical_sha256":"865b6c617cf6f80ab223fca1ebe2b0af68fd86108560ffae201322df769d2903","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:43.447562Z","signature_b64":"NczwnX9ArKKcuz48f6GVbnO7zD1sshWF2sP64RVnxIET7dd6J0DAZku7OouOynhxyeTAh64G4F+HgjT4w8GPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865b6c617cf6f80ab223fca1ebe2b0af68fd86108560ffae201322df769d2903","last_reissued_at":"2026-07-28T01:22:43.446812Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:43.446812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23240","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":"2026-07-28T01:22:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zNFtf8xgjoD1+dfBz7+K9i35UvSbAGfvUrZ3iY5Eu2/1+yboVcgqm1GfFX8sS/tHBeh3xMTgFHh2KIex7EjYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:09:17.250956Z"},"content_sha256":"5af6b5e76dccd98d11c784f16d0ab04efd397781c206db316a9c78ffb7b575f9","schema_version":"1.0","event_id":"sha256:5af6b5e76dccd98d11c784f16d0ab04efd397781c206db316a9c78ffb7b575f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QZNWYYL4634AVMRD7SQ6XYVQV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nested Integral Generator Theorem: From Operator Tautologies to Families of Exact Integral Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ghasem Asadi Cordshooli","submitted_at":"2026-07-25T14:53:28Z","abstract_excerpt":"Inserting resolutions of the identity is a standard technique for representing states and operators throughout quantum theory, quantum field theory, and related areas of mathematical physics. This paper elevates this procedure to a rigorous, representation-independent framework through the Nested Integral Generator Theorem. Starting from operator tautologies, the theorem systematically generates exact multi-fold integral identities by successive insertions of continuous resolutions of the identity followed by projection onto arbitrary orthonormal basis vectors. The resulting construction appli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23240","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/2607.23240/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":"2026-07-28T01:22:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9on7BXPz+rW/TcYsPiPGSd6XWrsrMLUNwHVeDuFqyGcltAN31vrSLZQPC6a9TCdSSGwBjWduKvht4JqGfYGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:09:17.251511Z"},"content_sha256":"f2fee713eaceadb50d8e35789aec78c6c1e8b8b4e67c7da9dfa7e1a45fbfaa54","schema_version":"1.0","event_id":"sha256:f2fee713eaceadb50d8e35789aec78c6c1e8b8b4e67c7da9dfa7e1a45fbfaa54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/bundle.json","state_url":"https://pith.science/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/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":"2026-08-13T14:09:17Z","links":{"resolver":"https://pith.science/pith/QZNWYYL4634AVMRD7SQ6XYVQV5","bundle":"https://pith.science/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/bundle.json","state":"https://pith.science/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZNWYYL4634AVMRD7SQ6XYVQV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QZNWYYL4634AVMRD7SQ6XYVQV5","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":"d6619ed4158cbbe6e2825372e5e96f90d04672dac1c27db2f13da1b264521a27","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-25T14:53:28Z","title_canon_sha256":"bd502523e1b4089e48a07eea108bfdea91c19b4c1c705dfb55215913871bff71"},"schema_version":"1.0","source":{"id":"2607.23240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23240","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23240v1","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23240","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_12","alias_value":"QZNWYYL4634A","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_16","alias_value":"QZNWYYL4634AVMRD","created_at":"2026-07-28T01:22:43Z"},{"alias_kind":"pith_short_8","alias_value":"QZNWYYL4","created_at":"2026-07-28T01:22:43Z"}],"graph_snapshots":[{"event_id":"sha256:f2fee713eaceadb50d8e35789aec78c6c1e8b8b4e67c7da9dfa7e1a45fbfaa54","target":"graph","created_at":"2026-07-28T01:22:43Z","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/2607.23240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inserting resolutions of the identity is a standard technique for representing states and operators throughout quantum theory, quantum field theory, and related areas of mathematical physics. This paper elevates this procedure to a rigorous, representation-independent framework through the Nested Integral Generator Theorem. Starting from operator tautologies, the theorem systematically generates exact multi-fold integral identities by successive insertions of continuous resolutions of the identity followed by projection onto arbitrary orthonormal basis vectors. The resulting construction appli","authors_text":"Ghasem Asadi Cordshooli","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-25T14:53:28Z","title":"Nested Integral Generator Theorem: From Operator Tautologies to Families of Exact Integral Identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23240","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":"sha256:5af6b5e76dccd98d11c784f16d0ab04efd397781c206db316a9c78ffb7b575f9","target":"record","created_at":"2026-07-28T01:22:43Z","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":"d6619ed4158cbbe6e2825372e5e96f90d04672dac1c27db2f13da1b264521a27","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-25T14:53:28Z","title_canon_sha256":"bd502523e1b4089e48a07eea108bfdea91c19b4c1c705dfb55215913871bff71"},"schema_version":"1.0","source":{"id":"2607.23240","kind":"arxiv","version":1}},"canonical_sha256":"865b6c617cf6f80ab223fca1ebe2b0af68fd86108560ffae201322df769d2903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865b6c617cf6f80ab223fca1ebe2b0af68fd86108560ffae201322df769d2903","first_computed_at":"2026-07-28T01:22:43.446812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:43.446812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NczwnX9ArKKcuz48f6GVbnO7zD1sshWF2sP64RVnxIET7dd6J0DAZku7OouOynhxyeTAh64G4F+HgjT4w8GPCw==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:43.447562Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5af6b5e76dccd98d11c784f16d0ab04efd397781c206db316a9c78ffb7b575f9","sha256:f2fee713eaceadb50d8e35789aec78c6c1e8b8b4e67c7da9dfa7e1a45fbfaa54"],"state_sha256":"8b13010f928c0bf3613bcae66ff8413426bb862e851ef4bf5cb5266b022ae641"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzu3sUuJYll9FaxzKuiv41iOSSHyc2kvlrlTY/sfKKpR5bC8mwWN1hhw9LC8JSUX2WV6bDnkSY1sT0BFbRw+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:09:17.256943Z","bundle_sha256":"faf1395f81d79ee76ef1722f63b613f2468953d5f49c24c2e9bf5055a8e481fa"}}