{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PW5AJWEIY6UZLGCGUOYNMILU5F","short_pith_number":"pith:PW5AJWEI","canonical_record":{"source":{"id":"1707.05448","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-07-18T03:14:38Z","cross_cats_sorted":["hep-th","math.AT"],"title_canon_sha256":"4eed10cd5d15c35602ea2bc63f2d2adc9499119c26359b9af6deee74e6c7a695","abstract_canon_sha256":"470e03e2d42f279e4a0b27fc9a07d4013399f30459220feec9d9ac4565e62793"},"schema_version":"1.0"},"canonical_sha256":"7dba04d888c7a9959846a3b0d62174e972f93185039418acb1b1aee6e0ce94b0","source":{"kind":"arxiv","id":"1707.05448","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05448","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05448v3","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05448","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"PW5AJWEIY6UZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PW5AJWEIY6UZLGCG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PW5AJWEI","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PW5AJWEIY6UZLGCGUOYNMILU5F","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05448","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-07-18T03:14:38Z","cross_cats_sorted":["hep-th","math.AT"],"title_canon_sha256":"4eed10cd5d15c35602ea2bc63f2d2adc9499119c26359b9af6deee74e6c7a695","abstract_canon_sha256":"470e03e2d42f279e4a0b27fc9a07d4013399f30459220feec9d9ac4565e62793"},"schema_version":"1.0"},"canonical_sha256":"7dba04d888c7a9959846a3b0d62174e972f93185039418acb1b1aee6e0ce94b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:13.362645Z","signature_b64":"qfxp59oVOpPet/ZS21k9XG4XPCoHBAZsqPWQj3d8CdKRgX2m/FGLGoqjCRdraIEeVUp0vYj9jwTcbeAP93A7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dba04d888c7a9959846a3b0d62174e972f93185039418acb1b1aee6e0ce94b0","last_reissued_at":"2026-05-18T00:21:13.362138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:13.362138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05448","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":"2026-05-18T00:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WxpAHyxZUt7+EBx8bzMRmfRJ+QGDD1sNxVf1TDjn0UbMxduoT4i6v1ItBBqxNutDny0qxqb/R0cDdy15N0KPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:46:55.671620Z"},"content_sha256":"5d0b27705453335dab69eb12450d696e55df170b037be752bd7faaf9804af636","schema_version":"1.0","event_id":"sha256:5d0b27705453335dab69eb12450d696e55df170b037be752bd7faaf9804af636"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PW5AJWEIY6UZLGCGUOYNMILU5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Sum Over Topological Sectors and $\\theta$ in the 2+1-Dimensional $\\mathbb{C}\\mathbb{P}^1$ $\\sigma$-Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AT"],"primary_cat":"cond-mat.str-el","authors_text":"Daniel S. Freed, Nathan Seiberg, Zohar Komargodski","submitted_at":"2017-07-18T03:14:38Z","abstract_excerpt":"We discuss the three spacetime dimensional $\\mathbb{C}\\mathbb{P}^N$ model and specialize to the $\\mathbb{C}\\mathbb{P}^1$ model. Because of the Hopf map $\\pi_3(\\mathbb{C}\\mathbb{P}^1)=\\mathbb{Z}$ one might try to couple the model to a periodic $\\theta$ parameter. However, we argue that only the values $\\theta=0$ and $\\theta=\\pi$ are consistent. For these values the Skyrmions in the model are bosons and fermions respectively, rather than being anyons. We also extend the model by coupling it to a topological quantum field theory, such that the Skyrmions are anyons. We use techniques from geometry"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05448","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":"2026-05-18T00:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bKbjskoQqBN2NYUruLyXk9O9Cdkye5FHMmd49RYVWE5AfRKeCFGXucb5Gwjc/8a41AJUZzq4vTlK1mQGlaDWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:46:55.672101Z"},"content_sha256":"5bda7709f77800c141b9b05191ca3604e15d48206a9b572c364496edbe3d3829","schema_version":"1.0","event_id":"sha256:5bda7709f77800c141b9b05191ca3604e15d48206a9b572c364496edbe3d3829"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/bundle.json","state_url":"https://pith.science/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/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":"2026-08-17T00:46:55Z","links":{"resolver":"https://pith.science/pith/PW5AJWEIY6UZLGCGUOYNMILU5F","bundle":"https://pith.science/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/bundle.json","state":"https://pith.science/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PW5AJWEIY6UZLGCGUOYNMILU5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PW5AJWEIY6UZLGCGUOYNMILU5F","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":"470e03e2d42f279e4a0b27fc9a07d4013399f30459220feec9d9ac4565e62793","cross_cats_sorted":["hep-th","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-07-18T03:14:38Z","title_canon_sha256":"4eed10cd5d15c35602ea2bc63f2d2adc9499119c26359b9af6deee74e6c7a695"},"schema_version":"1.0","source":{"id":"1707.05448","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05448","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05448v3","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05448","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"PW5AJWEIY6UZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PW5AJWEIY6UZLGCG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PW5AJWEI","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:5bda7709f77800c141b9b05191ca3604e15d48206a9b572c364496edbe3d3829","target":"graph","created_at":"2026-05-18T00:21:13Z","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 discuss the three spacetime dimensional $\\mathbb{C}\\mathbb{P}^N$ model and specialize to the $\\mathbb{C}\\mathbb{P}^1$ model. Because of the Hopf map $\\pi_3(\\mathbb{C}\\mathbb{P}^1)=\\mathbb{Z}$ one might try to couple the model to a periodic $\\theta$ parameter. However, we argue that only the values $\\theta=0$ and $\\theta=\\pi$ are consistent. For these values the Skyrmions in the model are bosons and fermions respectively, rather than being anyons. We also extend the model by coupling it to a topological quantum field theory, such that the Skyrmions are anyons. We use techniques from geometry","authors_text":"Daniel S. Freed, Nathan Seiberg, Zohar Komargodski","cross_cats":["hep-th","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-07-18T03:14:38Z","title":"The Sum Over Topological Sectors and $\\theta$ in the 2+1-Dimensional $\\mathbb{C}\\mathbb{P}^1$ $\\sigma$-Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05448","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":"sha256:5d0b27705453335dab69eb12450d696e55df170b037be752bd7faaf9804af636","target":"record","created_at":"2026-05-18T00:21:13Z","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":"470e03e2d42f279e4a0b27fc9a07d4013399f30459220feec9d9ac4565e62793","cross_cats_sorted":["hep-th","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-07-18T03:14:38Z","title_canon_sha256":"4eed10cd5d15c35602ea2bc63f2d2adc9499119c26359b9af6deee74e6c7a695"},"schema_version":"1.0","source":{"id":"1707.05448","kind":"arxiv","version":3}},"canonical_sha256":"7dba04d888c7a9959846a3b0d62174e972f93185039418acb1b1aee6e0ce94b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dba04d888c7a9959846a3b0d62174e972f93185039418acb1b1aee6e0ce94b0","first_computed_at":"2026-05-18T00:21:13.362138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:13.362138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qfxp59oVOpPet/ZS21k9XG4XPCoHBAZsqPWQj3d8CdKRgX2m/FGLGoqjCRdraIEeVUp0vYj9jwTcbeAP93A7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:13.362645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05448","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d0b27705453335dab69eb12450d696e55df170b037be752bd7faaf9804af636","sha256:5bda7709f77800c141b9b05191ca3604e15d48206a9b572c364496edbe3d3829"],"state_sha256":"684353f8d37af18928ce4781aeb404b900f7e24c1708da5910ea436c9f521b12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JJakWCWDjvOt60cbkQ79rury+1AEyenQ1apPW3Ux+iiArIXW4S3Ab1uBELLgq2Qd8r39KxTSjYCR4Kj1VIyDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:46:55.675591Z","bundle_sha256":"e19f0a06699e6bdb8dc1253435bd09e59733083d914d5348c22899490401ba8f"}}