{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JCIKC6KM2UHD3VLK7FJPAMTPCU","short_pith_number":"pith:JCIKC6KM","canonical_record":{"source":{"id":"1607.06041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:43:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"4115bf35461e585099c2bc48c291a2c957a4255b1875b8a82de5e8e096ebed8f","abstract_canon_sha256":"48e84d98641b10fe3b9dc37f3aec27f043c69e457a182e1c72d418be2c17cf8f"},"schema_version":"1.0"},"canonical_sha256":"4890a1794cd50e3dd56af952f0326f1530acd86aa2d04b7f250b5d227ff92f88","source":{"kind":"arxiv","id":"1607.06041","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06041","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06041v2","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06041","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"JCIKC6KM2UHD","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCIKC6KM2UHD3VLK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCIKC6KM","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JCIKC6KM2UHD3VLK7FJPAMTPCU","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:43:49Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"4115bf35461e585099c2bc48c291a2c957a4255b1875b8a82de5e8e096ebed8f","abstract_canon_sha256":"48e84d98641b10fe3b9dc37f3aec27f043c69e457a182e1c72d418be2c17cf8f"},"schema_version":"1.0"},"canonical_sha256":"4890a1794cd50e3dd56af952f0326f1530acd86aa2d04b7f250b5d227ff92f88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:57.262615Z","signature_b64":"LdpgnaMEsjIJ0pcWH66Da6sAxkwvnavcDzhkNWjW66l+XduorgbcxkHrzdFFePBNUEa5SJLLYDPmw+PCraoMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4890a1794cd50e3dd56af952f0326f1530acd86aa2d04b7f250b5d227ff92f88","last_reissued_at":"2026-05-18T01:09:57.261909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:57.261909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06041","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":"2026-05-18T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1oaGSEcQCNba9F8klvAUitUOF3GeOv5FXIyyU1uduGW50515bPqd3lHhYcFkQXPhuf2J6KBKt1G2Xe7yoKGOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:45:37.156739Z"},"content_sha256":"cad6df31e4e0ea955bb94317914ffbdd206bb6b96447b178e1cc6667d9da52ee","schema_version":"1.0","event_id":"sha256:cad6df31e4e0ea955bb94317914ffbdd206bb6b96447b178e1cc6667d9da52ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JCIKC6KM2UHD3VLK7FJPAMTPCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Planar algebras in braided tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Andr\\'e Henriques, David Penneys, James Tener","submitted_at":"2016-07-20T17:43:49Z","abstract_excerpt":"We generalize Jones' planar algebras by internalising the notion to a pivotal braided tensor category $\\mathcal{C}$. To formulate the notion, the planar tangles are now equipped with additional `anchor lines' which connect the inner circles to the outer circle. We call the resulting notion an anchored planar algebra. If we restrict to the case when $\\mathcal{C}$ is the category of vector spaces, then we recover the usual notion of a planar algebra. Building on our previous work on categorified traces, we prove that there is an equivalence of categories between anchored planar algebras in $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06041","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":"2026-05-18T01:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEdeLZvkqPgzmU6mYPfzbUEXrQpdvdJeA61u51jFZ2CWbNdYph+Z/vPQt/TbXn431LJcAQJR+XcYXHnne+02DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:45:37.157087Z"},"content_sha256":"709731b0f74e37ab0c566a2e991e2fe283bbdaf6f177c9bb523b9c9550f5eb3e","schema_version":"1.0","event_id":"sha256:709731b0f74e37ab0c566a2e991e2fe283bbdaf6f177c9bb523b9c9550f5eb3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/bundle.json","state_url":"https://pith.science/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/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":"2026-06-03T06:45:37Z","links":{"resolver":"https://pith.science/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU","bundle":"https://pith.science/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/bundle.json","state":"https://pith.science/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCIKC6KM2UHD3VLK7FJPAMTPCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JCIKC6KM2UHD3VLK7FJPAMTPCU","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":"48e84d98641b10fe3b9dc37f3aec27f043c69e457a182e1c72d418be2c17cf8f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:43:49Z","title_canon_sha256":"4115bf35461e585099c2bc48c291a2c957a4255b1875b8a82de5e8e096ebed8f"},"schema_version":"1.0","source":{"id":"1607.06041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06041","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06041v2","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06041","created_at":"2026-05-18T01:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"JCIKC6KM2UHD","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCIKC6KM2UHD3VLK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCIKC6KM","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:709731b0f74e37ab0c566a2e991e2fe283bbdaf6f177c9bb523b9c9550f5eb3e","target":"graph","created_at":"2026-05-18T01:09:57Z","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 Jones' planar algebras by internalising the notion to a pivotal braided tensor category $\\mathcal{C}$. To formulate the notion, the planar tangles are now equipped with additional `anchor lines' which connect the inner circles to the outer circle. We call the resulting notion an anchored planar algebra. If we restrict to the case when $\\mathcal{C}$ is the category of vector spaces, then we recover the usual notion of a planar algebra. Building on our previous work on categorified traces, we prove that there is an equivalence of categories between anchored planar algebras in $\\mat","authors_text":"Andr\\'e Henriques, David Penneys, James Tener","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:43:49Z","title":"Planar algebras in braided tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06041","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:cad6df31e4e0ea955bb94317914ffbdd206bb6b96447b178e1cc6667d9da52ee","target":"record","created_at":"2026-05-18T01:09:57Z","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":"48e84d98641b10fe3b9dc37f3aec27f043c69e457a182e1c72d418be2c17cf8f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T17:43:49Z","title_canon_sha256":"4115bf35461e585099c2bc48c291a2c957a4255b1875b8a82de5e8e096ebed8f"},"schema_version":"1.0","source":{"id":"1607.06041","kind":"arxiv","version":2}},"canonical_sha256":"4890a1794cd50e3dd56af952f0326f1530acd86aa2d04b7f250b5d227ff92f88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4890a1794cd50e3dd56af952f0326f1530acd86aa2d04b7f250b5d227ff92f88","first_computed_at":"2026-05-18T01:09:57.261909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:57.261909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdpgnaMEsjIJ0pcWH66Da6sAxkwvnavcDzhkNWjW66l+XduorgbcxkHrzdFFePBNUEa5SJLLYDPmw+PCraoMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:57.262615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cad6df31e4e0ea955bb94317914ffbdd206bb6b96447b178e1cc6667d9da52ee","sha256:709731b0f74e37ab0c566a2e991e2fe283bbdaf6f177c9bb523b9c9550f5eb3e"],"state_sha256":"72c097d7c38d1b5fd03cb14922f5eed514b926561ad8c5ea62a4ff858673d391"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hvFqY8ooIWs+rTndOAqI7vX9QWLaac92IeBbsGEA2vRZLXF3ZrvlkQDeIdjWosbhI9fEq9J6BB+NV1TTrMsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:45:37.159194Z","bundle_sha256":"19d3bd392e48ad77b10af7eca77a9c73d67161e6eb0b5a207bd58c2a68beb453"}}