{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q2PWY4GLO5FYTYIVA5MJJQQW7E","short_pith_number":"pith:Q2PWY4GL","canonical_record":{"source":{"id":"1211.2576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-12T11:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"ca0ea0fe6f168766aa849cac2e2b55ebbab47a638c49c7f410c021e3c85b1ee4","abstract_canon_sha256":"9ae92b032bdba15265fd73dcd20a1b529dd4b35f3de9d30ada6f25ba1c816a83"},"schema_version":"1.0"},"canonical_sha256":"869f6c70cb774b89e115075894c216f91e757d505b2f262c21b77aa5db26c663","source":{"kind":"arxiv","id":"1211.2576","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2576","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2576v3","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2576","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"Q2PWY4GLO5FY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q2PWY4GLO5FYTYIV","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q2PWY4GL","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q2PWY4GLO5FYTYIVA5MJJQQW7E","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-12T11:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"ca0ea0fe6f168766aa849cac2e2b55ebbab47a638c49c7f410c021e3c85b1ee4","abstract_canon_sha256":"9ae92b032bdba15265fd73dcd20a1b529dd4b35f3de9d30ada6f25ba1c816a83"},"schema_version":"1.0"},"canonical_sha256":"869f6c70cb774b89e115075894c216f91e757d505b2f262c21b77aa5db26c663","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:45.984013Z","signature_b64":"Hv3OyQ62Ivkg7P4eYhSKhg93nThcni+mIQiw40OrcaainYFrW9iz5pMICUpQu5Fm5ftmR24LbTblQ5/Co2wCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"869f6c70cb774b89e115075894c216f91e757d505b2f262c21b77aa5db26c663","last_reissued_at":"2026-05-18T03:10:45.983339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:45.983339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2576","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABKYn++Ps/VqsuAdbwq9Y82xDNR0lhWpYtVXDbaoPY1WrLvoRal9597r85HEcF8KjkVjZ5dchA9XZqLh9VgRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:28:15.775112Z"},"content_sha256":"c0a80bd3421de487cfa0f5b8d6bf9aba3c71db4f33fcb8a16b5923450b40b769","schema_version":"1.0","event_id":"sha256:c0a80bd3421de487cfa0f5b8d6bf9aba3c71db4f33fcb8a16b5923450b40b769"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q2PWY4GLO5FYTYIVA5MJJQQW7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extendable endomorphisms on factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Masaki Izumi, Panchugopal Bikram, R. Srinivasan, V. S. Sunder","submitted_at":"2012-11-12T11:25:47Z","abstract_excerpt":"We begin this note with a von Neumann algebraic version of the elementary but extremely useful fact about being able to extend inner-product preserving maps from a total set of the domain Hilbert space to an isometry defined on the entire domain. This leads us to the notion of when `good' endomorphisms of a factorial probability space $(M,\\phi)$ (which we call equi-modular) admit a natural extension to endomorphisms of $L^2(M,\\phi)$. We exhibit examples of such extendable endomorphisms.\n  We then pass to $E_0$-semigroups $\\alpha = {\\alpha_t: t \\geq 0}$ of factors, and observe that extendabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2576","kind":"arxiv","version":3},"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":"2026-05-18T03:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6l/Disc8w5e7PxMY3/SpzxPAjfyIs90gYW3pErgVKy3E8aPLMIspkTUq/2AsY1vnNmrbA5R37nhKTa3/iV6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:28:15.775828Z"},"content_sha256":"4213d2ad9759959aafe84547281d70df6ad83335acb652c6702e4351d22514e6","schema_version":"1.0","event_id":"sha256:4213d2ad9759959aafe84547281d70df6ad83335acb652c6702e4351d22514e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/bundle.json","state_url":"https://pith.science/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/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":"2026-05-28T20:28:15Z","links":{"resolver":"https://pith.science/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E","bundle":"https://pith.science/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/bundle.json","state":"https://pith.science/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2PWY4GLO5FYTYIVA5MJJQQW7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q2PWY4GLO5FYTYIVA5MJJQQW7E","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":"9ae92b032bdba15265fd73dcd20a1b529dd4b35f3de9d30ada6f25ba1c816a83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-12T11:25:47Z","title_canon_sha256":"ca0ea0fe6f168766aa849cac2e2b55ebbab47a638c49c7f410c021e3c85b1ee4"},"schema_version":"1.0","source":{"id":"1211.2576","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2576","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2576v3","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2576","created_at":"2026-05-18T03:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"Q2PWY4GLO5FY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q2PWY4GLO5FYTYIV","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q2PWY4GL","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:4213d2ad9759959aafe84547281d70df6ad83335acb652c6702e4351d22514e6","target":"graph","created_at":"2026-05-18T03:10:45Z","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 begin this note with a von Neumann algebraic version of the elementary but extremely useful fact about being able to extend inner-product preserving maps from a total set of the domain Hilbert space to an isometry defined on the entire domain. This leads us to the notion of when `good' endomorphisms of a factorial probability space $(M,\\phi)$ (which we call equi-modular) admit a natural extension to endomorphisms of $L^2(M,\\phi)$. We exhibit examples of such extendable endomorphisms.\n  We then pass to $E_0$-semigroups $\\alpha = {\\alpha_t: t \\geq 0}$ of factors, and observe that extendabilit","authors_text":"Masaki Izumi, Panchugopal Bikram, R. Srinivasan, V. S. Sunder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-12T11:25:47Z","title":"Extendable endomorphisms on factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2576","kind":"arxiv","version":3},"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:c0a80bd3421de487cfa0f5b8d6bf9aba3c71db4f33fcb8a16b5923450b40b769","target":"record","created_at":"2026-05-18T03:10:45Z","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":"9ae92b032bdba15265fd73dcd20a1b529dd4b35f3de9d30ada6f25ba1c816a83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-12T11:25:47Z","title_canon_sha256":"ca0ea0fe6f168766aa849cac2e2b55ebbab47a638c49c7f410c021e3c85b1ee4"},"schema_version":"1.0","source":{"id":"1211.2576","kind":"arxiv","version":3}},"canonical_sha256":"869f6c70cb774b89e115075894c216f91e757d505b2f262c21b77aa5db26c663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"869f6c70cb774b89e115075894c216f91e757d505b2f262c21b77aa5db26c663","first_computed_at":"2026-05-18T03:10:45.983339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:45.983339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hv3OyQ62Ivkg7P4eYhSKhg93nThcni+mIQiw40OrcaainYFrW9iz5pMICUpQu5Fm5ftmR24LbTblQ5/Co2wCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:45.984013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2576","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0a80bd3421de487cfa0f5b8d6bf9aba3c71db4f33fcb8a16b5923450b40b769","sha256:4213d2ad9759959aafe84547281d70df6ad83335acb652c6702e4351d22514e6"],"state_sha256":"8668753565f23159c30a2b820f93a75fbaf635eca56593b9ac3b6af67578e17e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbkYSgcuYpMfU7QzEdwknJ75NLzXrCPjLGZFub8eBKj0FtBkiENpZATUuGOBuPYHguJl3m5ujw55LIi9NGjQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:28:15.779935Z","bundle_sha256":"0063210b6d5a5bf21d373656c16b03bc02fdc1522f15839084a12d4c813d9007"}}