{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:IVV2HDPN3LGO3DL5DQUKB6EG3W","short_pith_number":"pith:IVV2HDPN","canonical_record":{"source":{"id":"math-ph/0206016","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-06-12T09:57:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"05e945c70f437dea37aeed0678bae66c34c1e2cd6853010c13416b785f39ac84","abstract_canon_sha256":"58e5e7f44dfa2b3f46d6ca4d3ec51f2b7e054000f2cee152e4338daf9c4ce42c"},"schema_version":"1.0"},"canonical_sha256":"456ba38deddacced8d7d1c28a0f886dd974d4fd7432f4a74e371f748fc903c2c","source":{"kind":"arxiv","id":"math-ph/0206016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0206016","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0206016v1","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0206016","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"IVV2HDPN3LGO","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IVV2HDPN3LGO3DL5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IVV2HDPN","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:IVV2HDPN3LGO3DL5DQUKB6EG3W","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0206016","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-06-12T09:57:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"05e945c70f437dea37aeed0678bae66c34c1e2cd6853010c13416b785f39ac84","abstract_canon_sha256":"58e5e7f44dfa2b3f46d6ca4d3ec51f2b7e054000f2cee152e4338daf9c4ce42c"},"schema_version":"1.0"},"canonical_sha256":"456ba38deddacced8d7d1c28a0f886dd974d4fd7432f4a74e371f748fc903c2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.150194Z","signature_b64":"iCjCR9lgtx3MfsO6gxHPouh2Xo1pnHT6o+ZiGGGudAIaqyRwcnhMOr92MY7rko09IP+EGpevixQgWMwI7NxlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"456ba38deddacced8d7d1c28a0f886dd974d4fd7432f4a74e371f748fc903c2c","last_reissued_at":"2026-05-18T01:38:34.149581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.149581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0206016","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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJaXsh/j0P6f+T9K+vGbt2vZqmlCcmYVFRmEBF9bm1il2dR8Dq745vKlpzrkjrNIclbYR+bkRHX6Sw/Fl37TDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:37:12.082478Z"},"content_sha256":"2d92347f0113ec2669c33e1ee191280249e3ba7fbbfad702ef9e7a4a1eb36b3e","schema_version":"1.0","event_id":"sha256:2d92347f0113ec2669c33e1ee191280249e3ba7fbbfad702ef9e7a4a1eb36b3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:IVV2HDPN3LGO3DL5DQUKB6EG3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Special Deformed Exponential Functions Leading to More Consistent Klauder's Coherent States","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"M. El Baz, Y. Hassouni","submitted_at":"2002-06-12T09:57:16Z","abstract_excerpt":"We give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary exponential functions in the limit when the deformation parameters goes to one. We also prove that these series converge to a complex function, in a given convergence radius that we calculate. Klauder's Coherent States are explicitly found through these functions that we design by deformed exponential functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0206016","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":""},"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":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQnzwpQcIBBaNaL/R0xEn9/R4ygiyDZSWlBXuTacyqyn67tPV1ZhWxs1t6p7qYxsoWIacWH0RGt3OdhvKhksDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:37:12.082824Z"},"content_sha256":"114715a103f82c93ff75d295a2ea2edb8d167c3c15d012777323e14b1d5b243d","schema_version":"1.0","event_id":"sha256:114715a103f82c93ff75d295a2ea2edb8d167c3c15d012777323e14b1d5b243d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/bundle.json","state_url":"https://pith.science/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/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":"2026-06-28T08:37:12Z","links":{"resolver":"https://pith.science/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W","bundle":"https://pith.science/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/bundle.json","state":"https://pith.science/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVV2HDPN3LGO3DL5DQUKB6EG3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:IVV2HDPN3LGO3DL5DQUKB6EG3W","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":"58e5e7f44dfa2b3f46d6ca4d3ec51f2b7e054000f2cee152e4338daf9c4ce42c","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-06-12T09:57:16Z","title_canon_sha256":"05e945c70f437dea37aeed0678bae66c34c1e2cd6853010c13416b785f39ac84"},"schema_version":"1.0","source":{"id":"math-ph/0206016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0206016","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0206016v1","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0206016","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"IVV2HDPN3LGO","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IVV2HDPN3LGO3DL5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IVV2HDPN","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:114715a103f82c93ff75d295a2ea2edb8d167c3c15d012777323e14b1d5b243d","target":"graph","created_at":"2026-05-18T01:38:34Z","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 give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary exponential functions in the limit when the deformation parameters goes to one. We also prove that these series converge to a complex function, in a given convergence radius that we calculate. Klauder's Coherent States are explicitly found through these functions that we design by deformed exponential functions","authors_text":"M. El Baz, Y. Hassouni","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-06-12T09:57:16Z","title":"Special Deformed Exponential Functions Leading to More Consistent Klauder's Coherent States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0206016","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":"sha256:2d92347f0113ec2669c33e1ee191280249e3ba7fbbfad702ef9e7a4a1eb36b3e","target":"record","created_at":"2026-05-18T01:38:34Z","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":"58e5e7f44dfa2b3f46d6ca4d3ec51f2b7e054000f2cee152e4338daf9c4ce42c","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-06-12T09:57:16Z","title_canon_sha256":"05e945c70f437dea37aeed0678bae66c34c1e2cd6853010c13416b785f39ac84"},"schema_version":"1.0","source":{"id":"math-ph/0206016","kind":"arxiv","version":1}},"canonical_sha256":"456ba38deddacced8d7d1c28a0f886dd974d4fd7432f4a74e371f748fc903c2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"456ba38deddacced8d7d1c28a0f886dd974d4fd7432f4a74e371f748fc903c2c","first_computed_at":"2026-05-18T01:38:34.149581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:34.149581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iCjCR9lgtx3MfsO6gxHPouh2Xo1pnHT6o+ZiGGGudAIaqyRwcnhMOr92MY7rko09IP+EGpevixQgWMwI7NxlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:34.150194Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0206016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d92347f0113ec2669c33e1ee191280249e3ba7fbbfad702ef9e7a4a1eb36b3e","sha256:114715a103f82c93ff75d295a2ea2edb8d167c3c15d012777323e14b1d5b243d"],"state_sha256":"5262f5acf0d97c4e74b5185ac5fcd811a40f65a74f063a542bbc681ad605bbb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZFlCP37+I/6mGu7tnVaU9AnfEQOHyBrBlkSvn1pv+sA+PDXRdyZ/AEUUGO1PHoWjfU/aIOUoostvsC3uUNoKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:37:12.084604Z","bundle_sha256":"30bcc8b8a5801fda3cb3517b96f5bb426d3f82c3c64c086b33c2fe7e0077bbf7"}}