{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3W7C5WV5T4XSHPRHKYH6LMQTKB","short_pith_number":"pith:3W7C5WV5","schema_version":"1.0","canonical_sha256":"ddbe2edabd9f2f23be27560fe5b213505d39ae2ed273e7babb06a4b66f9bd871","source":{"kind":"arxiv","id":"1210.2666","version":1},"attestation_state":"computed","paper":{"title":"An analytic family of representations for the mapping class group of punctured surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.GT","authors_text":"Bruno Martelli, Francesco Costantino","submitted_at":"2012-10-09T17:05:04Z","abstract_excerpt":"We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space. They are unitary when A is real or imaginary, bounded when |A|<1, and only densely defined when |A| = 1 and A is not a root of unity. When A is a root of unity distinct from 1, -1, i, -i the representations are finite-dimensional and isomorphic to the \"Hom\" version of the well-known TQFT quantum representations.\n  The unitary representations in the interval ["},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-09T17:05:04Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"9c0af4b2f9801820758dffc1118571012cd19e5527fcefec4ff0c99799c4f917","abstract_canon_sha256":"1af9da0f99c28ec1eb4444b7fa8596231d603601fb6d93f9556d98b3b3d7fc23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:17.612480Z","signature_b64":"m1AP3N63veqTLaCJVlPbz0He8liymnsAp8MhB7Wyqby84dAKZN4TNU++sGIA8HDosQ2GG63y0JEfBm16yR3RBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddbe2edabd9f2f23be27560fe5b213505d39ae2ed273e7babb06a4b66f9bd871","last_reissued_at":"2026-05-18T02:38:17.611827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:17.611827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analytic family of representations for the mapping class group of punctured surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.GT","authors_text":"Bruno Martelli, Francesco Costantino","submitted_at":"2012-10-09T17:05:04Z","abstract_excerpt":"We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space. They are unitary when A is real or imaginary, bounded when |A|<1, and only densely defined when |A| = 1 and A is not a root of unity. When A is a root of unity distinct from 1, -1, i, -i the representations are finite-dimensional and isomorphic to the \"Hom\" version of the well-known TQFT quantum representations.\n  The unitary representations in the interval ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2666","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.2666","created_at":"2026-05-18T02:38:17.611918+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2666v1","created_at":"2026-05-18T02:38:17.611918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2666","created_at":"2026-05-18T02:38:17.611918+00:00"},{"alias_kind":"pith_short_12","alias_value":"3W7C5WV5T4XS","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3W7C5WV5T4XSHPRH","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3W7C5WV5","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB","json":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB.json","graph_json":"https://pith.science/api/pith-number/3W7C5WV5T4XSHPRHKYH6LMQTKB/graph.json","events_json":"https://pith.science/api/pith-number/3W7C5WV5T4XSHPRHKYH6LMQTKB/events.json","paper":"https://pith.science/paper/3W7C5WV5"},"agent_actions":{"view_html":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB","download_json":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB.json","view_paper":"https://pith.science/paper/3W7C5WV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2666&json=true","fetch_graph":"https://pith.science/api/pith-number/3W7C5WV5T4XSHPRHKYH6LMQTKB/graph.json","fetch_events":"https://pith.science/api/pith-number/3W7C5WV5T4XSHPRHKYH6LMQTKB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB/action/storage_attestation","attest_author":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB/action/author_attestation","sign_citation":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB/action/citation_signature","submit_replication":"https://pith.science/pith/3W7C5WV5T4XSHPRHKYH6LMQTKB/action/replication_record"}},"created_at":"2026-05-18T02:38:17.611918+00:00","updated_at":"2026-05-18T02:38:17.611918+00:00"}