{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6LQQEQORAGRBWCQUN4ZPR76YSI","short_pith_number":"pith:6LQQEQOR","canonical_record":{"source":{"id":"1007.0798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T02:44:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dc7f75546c461a9f787dc3b27913197d63a17d4c0b0da028279f8be8ec68e654","abstract_canon_sha256":"67610565f8d30494539d3030f9fed8df54879dbb111db7509e16e64cae457f6c"},"schema_version":"1.0"},"canonical_sha256":"f2e10241d101a21b0a146f32f8ffd8922c5bc35749ccc90d19dc333c162932b2","source":{"kind":"arxiv","id":"1007.0798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0798","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0798v1","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0798","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"6LQQEQORAGRB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6LQQEQORAGRBWCQU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6LQQEQOR","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6LQQEQORAGRBWCQUN4ZPR76YSI","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T02:44:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dc7f75546c461a9f787dc3b27913197d63a17d4c0b0da028279f8be8ec68e654","abstract_canon_sha256":"67610565f8d30494539d3030f9fed8df54879dbb111db7509e16e64cae457f6c"},"schema_version":"1.0"},"canonical_sha256":"f2e10241d101a21b0a146f32f8ffd8922c5bc35749ccc90d19dc333c162932b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:32.200780Z","signature_b64":"KWKsMXIHLmqsMSDekx6nQETynqpZrSbnfwJWAMiJL/JAQDr+dcgImXHoywVHsxtjDLr/VFryPHMqXiK0fZSZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2e10241d101a21b0a146f32f8ffd8922c5bc35749ccc90d19dc333c162932b2","last_reissued_at":"2026-05-18T02:06:32.200069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:32.200069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0798","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":"2026-05-18T02:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSREiX9RPZUdfY8k0tm/YR3TIM+XpYLvo9ttOztTSmhfIX9i0TSicqdJyU6/4tUsAZbwfAJlaTTVme4C21bbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:23:48.167022Z"},"content_sha256":"393ca6fe97d12c4391d6a88130c08e17fb93e121b9e9cf74408ade893f5580c8","schema_version":"1.0","event_id":"sha256:393ca6fe97d12c4391d6a88130c08e17fb93e121b9e9cf74408ade893f5580c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6LQQEQORAGRBWCQUN4ZPR76YSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherent States on Hilbert Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"S. Shyam Roy, S. Twareque Ali, T. Bhattacharyya","submitted_at":"2010-07-06T02:44:43Z","abstract_excerpt":"We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0798","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":"2026-05-18T02:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6iav8PcepM941AN5uPfJic/0yf1tlvQCoXOu5EeexcXOWQy7zrCiShy7xvsSnSVVlskDCz41lh3kzgtECUGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:23:48.167393Z"},"content_sha256":"a3ffc2aa24cc83e5bfd819ee639820769ff4d03ce417ac8d42b1fe25640bcb38","schema_version":"1.0","event_id":"sha256:a3ffc2aa24cc83e5bfd819ee639820769ff4d03ce417ac8d42b1fe25640bcb38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/bundle.json","state_url":"https://pith.science/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/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":"2026-06-01T16:23:48Z","links":{"resolver":"https://pith.science/pith/6LQQEQORAGRBWCQUN4ZPR76YSI","bundle":"https://pith.science/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/bundle.json","state":"https://pith.science/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LQQEQORAGRBWCQUN4ZPR76YSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6LQQEQORAGRBWCQUN4ZPR76YSI","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":"67610565f8d30494539d3030f9fed8df54879dbb111db7509e16e64cae457f6c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T02:44:43Z","title_canon_sha256":"dc7f75546c461a9f787dc3b27913197d63a17d4c0b0da028279f8be8ec68e654"},"schema_version":"1.0","source":{"id":"1007.0798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0798","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0798v1","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0798","created_at":"2026-05-18T02:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"6LQQEQORAGRB","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6LQQEQORAGRBWCQU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6LQQEQOR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a3ffc2aa24cc83e5bfd819ee639820769ff4d03ce417ac8d42b1fe25640bcb38","target":"graph","created_at":"2026-05-18T02:06:32Z","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 generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples ","authors_text":"S. Shyam Roy, S. Twareque Ali, T. Bhattacharyya","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T02:44:43Z","title":"Coherent States on Hilbert Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0798","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":"sha256:393ca6fe97d12c4391d6a88130c08e17fb93e121b9e9cf74408ade893f5580c8","target":"record","created_at":"2026-05-18T02:06:32Z","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":"67610565f8d30494539d3030f9fed8df54879dbb111db7509e16e64cae457f6c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T02:44:43Z","title_canon_sha256":"dc7f75546c461a9f787dc3b27913197d63a17d4c0b0da028279f8be8ec68e654"},"schema_version":"1.0","source":{"id":"1007.0798","kind":"arxiv","version":1}},"canonical_sha256":"f2e10241d101a21b0a146f32f8ffd8922c5bc35749ccc90d19dc333c162932b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2e10241d101a21b0a146f32f8ffd8922c5bc35749ccc90d19dc333c162932b2","first_computed_at":"2026-05-18T02:06:32.200069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:32.200069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KWKsMXIHLmqsMSDekx6nQETynqpZrSbnfwJWAMiJL/JAQDr+dcgImXHoywVHsxtjDLr/VFryPHMqXiK0fZSZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:32.200780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:393ca6fe97d12c4391d6a88130c08e17fb93e121b9e9cf74408ade893f5580c8","sha256:a3ffc2aa24cc83e5bfd819ee639820769ff4d03ce417ac8d42b1fe25640bcb38"],"state_sha256":"f133420912e1a1d7b699e24e422ee0238cb6f066e2bc1908bfd951f81d0388b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9kaphmlUf/u1XCNOr6uP0nTAFy1vVRl6dAHXRutPQbVc36mE+ABYhbUTMUsFivafyg7lUwyv+BxtZYLQmc+3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:23:48.169368Z","bundle_sha256":"7bf9d13df435cef390dd1cde97c147ad5d57089fd6252ef045cf20e1d7173703"}}