{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7OW5N2WR3NALT4PYTGGGC5O53U","short_pith_number":"pith:7OW5N2WR","canonical_record":{"source":{"id":"1704.06957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-23T18:24:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"39d501176ea35fdaa04e4bd1227f4abae8ddb344f1debcc6a8e57d752808827e","abstract_canon_sha256":"726f91ffcd42613fd4e11eb0ebf2af09801648271d06c496607002f02e2fd09c"},"schema_version":"1.0"},"canonical_sha256":"fbadd6ead1db40b9f1f8998c6175dddd24b7a0c61d704aeb9460eef7406906de","source":{"kind":"arxiv","id":"1704.06957","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06957","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06957v2","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06957","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"7OW5N2WR3NAL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7OW5N2WR3NALT4PY","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7OW5N2WR","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7OW5N2WR3NALT4PYTGGGC5O53U","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-23T18:24:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"39d501176ea35fdaa04e4bd1227f4abae8ddb344f1debcc6a8e57d752808827e","abstract_canon_sha256":"726f91ffcd42613fd4e11eb0ebf2af09801648271d06c496607002f02e2fd09c"},"schema_version":"1.0"},"canonical_sha256":"fbadd6ead1db40b9f1f8998c6175dddd24b7a0c61d704aeb9460eef7406906de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:10.544261Z","signature_b64":"1eUYC/IPDRXmOSmO8rTBzccZn40jop7ixjoUNCi5fRzFuBNoLEU6LJqv3HfdZmRw9OmQKb3srN8c8qD0cBBJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbadd6ead1db40b9f1f8998c6175dddd24b7a0c61d704aeb9460eef7406906de","last_reissued_at":"2026-05-18T00:01:10.543520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:10.543520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06957","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":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rCJ7fZsOa1OqRRf4+/2qe+NVZIKg8SkSvycjRePgnno+ZjcXuj8A/ZbE2jjxlbWMQbfe4k5CYwoZVcYTCVNTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:55:32.124417Z"},"content_sha256":"aa4c4ad100f3a32139d7681bec62b45345d118fe53b81899d11d0b7deb00e501","schema_version":"1.0","event_id":"sha256:aa4c4ad100f3a32139d7681bec62b45345d118fe53b81899d11d0b7deb00e501"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7OW5N2WR3NALT4PYTGGGC5O53U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy of an autoequivalence on Calabi-Yau manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Yu-Wei Fan","submitted_at":"2017-04-23T18:24:50Z","abstract_excerpt":"We prove that the categorical entropy of the autoequivalence $T_{\\mathcal{O}}\\circ(-\\otimes\\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\\lambda$ satisfying $$ \\sum_{k\\geq 1}\\frac{\\chi(\\mathcal{O}(k))}{e^{k\\lambda}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06957","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":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HVi9+5mcvYeJ3QvV0V6DaDEI2RM2HyZw97+5TuaAJyeSQaNhCGjMNvWvdc5DkC1O/bE66eoDdagUOu7VJu6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:55:32.124991Z"},"content_sha256":"9ce8d903fbe7bde1fb20fece762b34468d7b588677ff7096f401a5cf4f7f69eb","schema_version":"1.0","event_id":"sha256:9ce8d903fbe7bde1fb20fece762b34468d7b588677ff7096f401a5cf4f7f69eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OW5N2WR3NALT4PYTGGGC5O53U/bundle.json","state_url":"https://pith.science/pith/7OW5N2WR3NALT4PYTGGGC5O53U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OW5N2WR3NALT4PYTGGGC5O53U/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":"2026-08-07T10:55:32Z","links":{"resolver":"https://pith.science/pith/7OW5N2WR3NALT4PYTGGGC5O53U","bundle":"https://pith.science/pith/7OW5N2WR3NALT4PYTGGGC5O53U/bundle.json","state":"https://pith.science/pith/7OW5N2WR3NALT4PYTGGGC5O53U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OW5N2WR3NALT4PYTGGGC5O53U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7OW5N2WR3NALT4PYTGGGC5O53U","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":"726f91ffcd42613fd4e11eb0ebf2af09801648271d06c496607002f02e2fd09c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-23T18:24:50Z","title_canon_sha256":"39d501176ea35fdaa04e4bd1227f4abae8ddb344f1debcc6a8e57d752808827e"},"schema_version":"1.0","source":{"id":"1704.06957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06957","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06957v2","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06957","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"7OW5N2WR3NAL","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7OW5N2WR3NALT4PY","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7OW5N2WR","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:9ce8d903fbe7bde1fb20fece762b34468d7b588677ff7096f401a5cf4f7f69eb","target":"graph","created_at":"2026-05-18T00:01:10Z","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 prove that the categorical entropy of the autoequivalence $T_{\\mathcal{O}}\\circ(-\\otimes\\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\\lambda$ satisfying $$ \\sum_{k\\geq 1}\\frac{\\chi(\\mathcal{O}(k))}{e^{k\\lambda}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.","authors_text":"Yu-Wei Fan","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-23T18:24:50Z","title":"Entropy of an autoequivalence on Calabi-Yau manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06957","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:aa4c4ad100f3a32139d7681bec62b45345d118fe53b81899d11d0b7deb00e501","target":"record","created_at":"2026-05-18T00:01:10Z","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":"726f91ffcd42613fd4e11eb0ebf2af09801648271d06c496607002f02e2fd09c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-23T18:24:50Z","title_canon_sha256":"39d501176ea35fdaa04e4bd1227f4abae8ddb344f1debcc6a8e57d752808827e"},"schema_version":"1.0","source":{"id":"1704.06957","kind":"arxiv","version":2}},"canonical_sha256":"fbadd6ead1db40b9f1f8998c6175dddd24b7a0c61d704aeb9460eef7406906de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbadd6ead1db40b9f1f8998c6175dddd24b7a0c61d704aeb9460eef7406906de","first_computed_at":"2026-05-18T00:01:10.543520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:10.543520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1eUYC/IPDRXmOSmO8rTBzccZn40jop7ixjoUNCi5fRzFuBNoLEU6LJqv3HfdZmRw9OmQKb3srN8c8qD0cBBJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:10.544261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa4c4ad100f3a32139d7681bec62b45345d118fe53b81899d11d0b7deb00e501","sha256:9ce8d903fbe7bde1fb20fece762b34468d7b588677ff7096f401a5cf4f7f69eb"],"state_sha256":"1fbe6d606a8774d84a73e09b8a82a44711facddf9bfdb387134cc2a4219da2a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ajeBPbsieHsgTTBklYKOsKeAvJl0Fg1OME6BvydU9G4xMGGlxLpkqz+y8zw1cjBGTpXCf2Ze+9JIURhIiYhEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:55:32.129705Z","bundle_sha256":"25f39987470dcf32f6571c00b2d78f3bdbbe566ae5bec74c67dc103efd3a0e1a"}}