{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V7U33AQQCRLAQ6IF6CM7IPGEYZ","short_pith_number":"pith:V7U33AQQ","canonical_record":{"source":{"id":"1603.05551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-17T16:06:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0f167838e2095af02a91d0303d910f97c09ca069a7a232be9960874725ebb914","abstract_canon_sha256":"6ffea3a294767609c4d62f447e71a45fcd8926190284ad148a1d25c073bac78c"},"schema_version":"1.0"},"canonical_sha256":"afe9bd82101456087905f099f43cc4c65ea7f1c4e8f644b6e189e8238e2478a6","source":{"kind":"arxiv","id":"1603.05551","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05551","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05551v2","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05551","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"V7U33AQQCRLA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7U33AQQCRLAQ6IF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7U33AQQ","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V7U33AQQCRLAQ6IF6CM7IPGEYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-17T16:06:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0f167838e2095af02a91d0303d910f97c09ca069a7a232be9960874725ebb914","abstract_canon_sha256":"6ffea3a294767609c4d62f447e71a45fcd8926190284ad148a1d25c073bac78c"},"schema_version":"1.0"},"canonical_sha256":"afe9bd82101456087905f099f43cc4c65ea7f1c4e8f644b6e189e8238e2478a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:06.338399Z","signature_b64":"Er7wXfBWsoVmpvsfoaL1IT36u9hbj/EvqZvyuRBdqljyNGsO/veWTILo9gEy4bgq+BA5eMq80dHv856knAyvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afe9bd82101456087905f099f43cc4c65ea7f1c4e8f644b6e189e8238e2478a6","last_reissued_at":"2026-05-18T01:10:06.337847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:06.337847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05551","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPXT1aTDZ+rZwkXDqNTvCcodch5GRS9GMa/ZH+TWvH1nKToj7B4gYCFBLTZWcIsD5FGsNazG2rT4lJxoBEXWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:25:15.504697Z"},"content_sha256":"0c626307ef60ffc52067fa6b82e5c82f588282058d829ad99602b0a642d199bc","schema_version":"1.0","event_id":"sha256:0c626307ef60ffc52067fa6b82e5c82f588282058d829ad99602b0a642d199bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V7U33AQQCRLAQ6IF6CM7IPGEYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projectors and seed conformal blocks for traceless mixed-symmetry tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Emilio Trevisani, Jo\\~ao Penedones, Miguel S. Costa, Tobias Hansen","submitted_at":"2016-03-17T16:06:41Z","abstract_excerpt":"In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05551","kind":"arxiv","version":2},"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":"2026-05-18T01:10:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7GXsILCXB6fZnGGl7GUjtheXgWL96VLLx13n3DvZvoV4Xi0j/g2BJ8qUIkm07TYSRuxl8Cu7uZIxgnPmNVdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:25:15.505057Z"},"content_sha256":"5b53fd307d45db4db285311344635ef066e2620bcfe7bc86296b926c6392ff6d","schema_version":"1.0","event_id":"sha256:5b53fd307d45db4db285311344635ef066e2620bcfe7bc86296b926c6392ff6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/bundle.json","state_url":"https://pith.science/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/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":"2026-05-27T09:25:15Z","links":{"resolver":"https://pith.science/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ","bundle":"https://pith.science/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/bundle.json","state":"https://pith.science/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7U33AQQCRLAQ6IF6CM7IPGEYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V7U33AQQCRLAQ6IF6CM7IPGEYZ","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":"6ffea3a294767609c4d62f447e71a45fcd8926190284ad148a1d25c073bac78c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-17T16:06:41Z","title_canon_sha256":"0f167838e2095af02a91d0303d910f97c09ca069a7a232be9960874725ebb914"},"schema_version":"1.0","source":{"id":"1603.05551","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05551","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05551v2","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05551","created_at":"2026-05-18T01:10:06Z"},{"alias_kind":"pith_short_12","alias_value":"V7U33AQQCRLA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7U33AQQCRLAQ6IF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7U33AQQ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:5b53fd307d45db4db285311344635ef066e2620bcfe7bc86296b926c6392ff6d","target":"graph","created_at":"2026-05-18T01:10:06Z","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":"In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization cons","authors_text":"Emilio Trevisani, Jo\\~ao Penedones, Miguel S. Costa, Tobias Hansen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-17T16:06:41Z","title":"Projectors and seed conformal blocks for traceless mixed-symmetry tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05551","kind":"arxiv","version":2},"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":"sha256:0c626307ef60ffc52067fa6b82e5c82f588282058d829ad99602b0a642d199bc","target":"record","created_at":"2026-05-18T01:10:06Z","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":"6ffea3a294767609c4d62f447e71a45fcd8926190284ad148a1d25c073bac78c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-03-17T16:06:41Z","title_canon_sha256":"0f167838e2095af02a91d0303d910f97c09ca069a7a232be9960874725ebb914"},"schema_version":"1.0","source":{"id":"1603.05551","kind":"arxiv","version":2}},"canonical_sha256":"afe9bd82101456087905f099f43cc4c65ea7f1c4e8f644b6e189e8238e2478a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afe9bd82101456087905f099f43cc4c65ea7f1c4e8f644b6e189e8238e2478a6","first_computed_at":"2026-05-18T01:10:06.337847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:06.337847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Er7wXfBWsoVmpvsfoaL1IT36u9hbj/EvqZvyuRBdqljyNGsO/veWTILo9gEy4bgq+BA5eMq80dHv856knAyvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:06.338399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05551","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c626307ef60ffc52067fa6b82e5c82f588282058d829ad99602b0a642d199bc","sha256:5b53fd307d45db4db285311344635ef066e2620bcfe7bc86296b926c6392ff6d"],"state_sha256":"43446479f58a09d356bbb4d37a96c7472d1a0a2372e4e204663261ea33732d45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QsTLaX4z0IraHpi5j/Ib8M3zKYTWW5Caf/nRXnrtwgTC0eHv2CQgKhBVLaygWTOcCZB8+7EoXPRjUBKf+Ha5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:25:15.507834Z","bundle_sha256":"6d687ab2c42231f275a1bdf4bc071afe986808246a410cfa2876abeb210f73c5"}}