{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:ENEBSYFEIO56UQJ4F3K56BT7C6","short_pith_number":"pith:ENEBSYFE","canonical_record":{"source":{"id":"chao-dyn/9606012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1996-06-27T22:52:53Z","cross_cats_sorted":["cond-mat","nlin.CD"],"title_canon_sha256":"23de37392a7cb63b1d8d987b7e070dcbe2ae4d37b918cc82641d373d9ddc95af","abstract_canon_sha256":"aa2fdcfc920b0c4feb1d44f578471a83756dfa364f054cd34c96d1eaac5ce0ec"},"schema_version":"1.0"},"canonical_sha256":"23481960a443bbea413c2ed5df067f179a0153293853dcc73ffcb4579577e555","source":{"kind":"arxiv","id":"chao-dyn/9606012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9606012","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9606012v1","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9606012","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"ENEBSYFEIO56","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_16","alias_value":"ENEBSYFEIO56UQJ4","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_8","alias_value":"ENEBSYFE","created_at":"2026-07-04T16:00:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:ENEBSYFEIO56UQJ4F3K56BT7C6","target":"record","payload":{"canonical_record":{"source":{"id":"chao-dyn/9606012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1996-06-27T22:52:53Z","cross_cats_sorted":["cond-mat","nlin.CD"],"title_canon_sha256":"23de37392a7cb63b1d8d987b7e070dcbe2ae4d37b918cc82641d373d9ddc95af","abstract_canon_sha256":"aa2fdcfc920b0c4feb1d44f578471a83756dfa364f054cd34c96d1eaac5ce0ec"},"schema_version":"1.0"},"canonical_sha256":"23481960a443bbea413c2ed5df067f179a0153293853dcc73ffcb4579577e555","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:00:23.528868Z","signature_b64":"9vD73LYIjM8hzCz6gqcmlIBXyFf67vTYLcemD9dNvDQclOec1W5mC9D8uPoNd7KzlFd0bNt9bx0vXlQAq+XaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23481960a443bbea413c2ed5df067f179a0153293853dcc73ffcb4579577e555","last_reissued_at":"2026-07-04T16:00:23.528464Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:00:23.528464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"chao-dyn/9606012","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":"2026-07-04T16:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXsryENr++Qe/5z+jsNSjykdURiWE1sOGrV7VvSIWEIBA74Ps0dXo0dEZQeW0wM7CfkfGhDOJskqzmT3dfRQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:36:03.916550Z"},"content_sha256":"58b8b1a531b747bf2b3012ad9773f493f3b9a0b5f732443d26e1a370b11498dd","schema_version":"1.0","event_id":"sha256:58b8b1a531b747bf2b3012ad9773f493f3b9a0b5f732443d26e1a370b11498dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:ENEBSYFEIO56UQJ4F3K56BT7C6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of roots of random real generalized polynomials","license":"","headline":"","cross_cats":["cond-mat","nlin.CD"],"primary_cat":"chao-dyn","authors_text":"CE Saclay, Daniel Bessis, France), Francisc D. Aaron (SPhT, G. Andrei Mezincescu, Giorgio Mantica, Jean-Daniel Fournier","submitted_at":"1996-06-27T22:52:53Z","abstract_excerpt":"The average density of zeros for monic generalized polynomials, $P_n(z)=\\phi(z)+\\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\\hbox{\\rm Im}\\,z|$. We present the low and high disorder asymptotic behaviors. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9606012","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/chao-dyn/9606012/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":"2026-07-04T16:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxtjGEdq4g4gEtT+AOHCGiZn5iQUstWMclxMxApAxuhjP4aarBLk60VtbdRu53vT2tlFdwYT8GQhnkYcvuV6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:36:03.917530Z"},"content_sha256":"9d375ae09cafa04525c725d69cc7e43eb690f063d460e717063664d8916aefae","schema_version":"1.0","event_id":"sha256:9d375ae09cafa04525c725d69cc7e43eb690f063d460e717063664d8916aefae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/bundle.json","state_url":"https://pith.science/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/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":"2026-08-13T21:36:03Z","links":{"resolver":"https://pith.science/pith/ENEBSYFEIO56UQJ4F3K56BT7C6","bundle":"https://pith.science/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/bundle.json","state":"https://pith.science/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENEBSYFEIO56UQJ4F3K56BT7C6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:ENEBSYFEIO56UQJ4F3K56BT7C6","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":"aa2fdcfc920b0c4feb1d44f578471a83756dfa364f054cd34c96d1eaac5ce0ec","cross_cats_sorted":["cond-mat","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1996-06-27T22:52:53Z","title_canon_sha256":"23de37392a7cb63b1d8d987b7e070dcbe2ae4d37b918cc82641d373d9ddc95af"},"schema_version":"1.0","source":{"id":"chao-dyn/9606012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9606012","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9606012v1","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9606012","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"ENEBSYFEIO56","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_16","alias_value":"ENEBSYFEIO56UQJ4","created_at":"2026-07-04T16:00:23Z"},{"alias_kind":"pith_short_8","alias_value":"ENEBSYFE","created_at":"2026-07-04T16:00:23Z"}],"graph_snapshots":[{"event_id":"sha256:9d375ae09cafa04525c725d69cc7e43eb690f063d460e717063664d8916aefae","target":"graph","created_at":"2026-07-04T16:00:23Z","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/chao-dyn/9606012/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The average density of zeros for monic generalized polynomials, $P_n(z)=\\phi(z)+\\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\\hbox{\\rm Im}\\,z|$. We present the low and high disorder asymptotic behaviors. Th","authors_text":"CE Saclay, Daniel Bessis, France), Francisc D. Aaron (SPhT, G. Andrei Mezincescu, Giorgio Mantica, Jean-Daniel Fournier","cross_cats":["cond-mat","nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1996-06-27T22:52:53Z","title":"Distribution of roots of random real generalized polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9606012","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":"sha256:58b8b1a531b747bf2b3012ad9773f493f3b9a0b5f732443d26e1a370b11498dd","target":"record","created_at":"2026-07-04T16:00:23Z","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":"aa2fdcfc920b0c4feb1d44f578471a83756dfa364f054cd34c96d1eaac5ce0ec","cross_cats_sorted":["cond-mat","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1996-06-27T22:52:53Z","title_canon_sha256":"23de37392a7cb63b1d8d987b7e070dcbe2ae4d37b918cc82641d373d9ddc95af"},"schema_version":"1.0","source":{"id":"chao-dyn/9606012","kind":"arxiv","version":1}},"canonical_sha256":"23481960a443bbea413c2ed5df067f179a0153293853dcc73ffcb4579577e555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23481960a443bbea413c2ed5df067f179a0153293853dcc73ffcb4579577e555","first_computed_at":"2026-07-04T16:00:23.528464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:00:23.528464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vD73LYIjM8hzCz6gqcmlIBXyFf67vTYLcemD9dNvDQclOec1W5mC9D8uPoNd7KzlFd0bNt9bx0vXlQAq+XaBw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:00:23.528868Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9606012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58b8b1a531b747bf2b3012ad9773f493f3b9a0b5f732443d26e1a370b11498dd","sha256:9d375ae09cafa04525c725d69cc7e43eb690f063d460e717063664d8916aefae"],"state_sha256":"de8ece29f4bce9717232c0d3bb8b1e1721d328cee0e39f28ca1241ed82b3c6ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vo8R/RKRtJxNaa2JUkR1zie6rGTgK8MtpIZLf6rXqa8KoldRkpH8XpQmtVNjYCdFwQtR7mSjMASrWrlErnsIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:36:03.990864Z","bundle_sha256":"84136b741871b97c385347e75b1b3a5c365ebd1344e98ef9b467cffb5cab8562"}}