{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MHDD4AEZLTQJNGBJ6BH5SCZK34","short_pith_number":"pith:MHDD4AEZ","canonical_record":{"source":{"id":"1110.1612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-07T19:17:53Z","cross_cats_sorted":[],"title_canon_sha256":"9bb422c1e64e9f9b7031b65cc987b0d43f4ff5063767725f3fecc44b844535f0","abstract_canon_sha256":"650226998183638714762e0fe9aeeee7caeff5ba4ce53eb101c51f81f8958d85"},"schema_version":"1.0"},"canonical_sha256":"61c63e00995ce0969829f04fd90b2adf3654a93d5e83cbda4480b64b9a7fc8e7","source":{"kind":"arxiv","id":"1110.1612","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1612","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1612v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1612","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"MHDD4AEZLTQJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MHDD4AEZLTQJNGBJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MHDD4AEZ","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MHDD4AEZLTQJNGBJ6BH5SCZK34","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-07T19:17:53Z","cross_cats_sorted":[],"title_canon_sha256":"9bb422c1e64e9f9b7031b65cc987b0d43f4ff5063767725f3fecc44b844535f0","abstract_canon_sha256":"650226998183638714762e0fe9aeeee7caeff5ba4ce53eb101c51f81f8958d85"},"schema_version":"1.0"},"canonical_sha256":"61c63e00995ce0969829f04fd90b2adf3654a93d5e83cbda4480b64b9a7fc8e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.913199Z","signature_b64":"O+ziYM9CXK7ePHf94GqE3qeAZyGg42BVMgLdMwuVgHxv2LaeTGxzLUtXD8c7rk+atpaWSFQRFKqvwwIm9HkQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61c63e00995ce0969829f04fd90b2adf3654a93d5e83cbda4480b64b9a7fc8e7","last_reissued_at":"2026-05-18T00:50:13.912737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.912737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1612","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkz2/EPxg8fEBw+UPMRRs1DDIRojbTzXTX0f1dtXygYUrhQ6EnXY5zlsTYnKVwv3M42WCMRkOg9tPrprRQ/tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:44:44.262692Z"},"content_sha256":"e0e1880b7e562e677127ec9844f21846f0e253588cd28e1b66a81fca5de15e18","schema_version":"1.0","event_id":"sha256:e0e1880b7e562e677127ec9844f21846f0e253588cd28e1b66a81fca5de15e18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MHDD4AEZLTQJNGBJ6BH5SCZK34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calabi-Yau Three-folds: Poincare Polynomials and Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Anthony Ashmore, Yang-Hui He","submitted_at":"2011-10-07T19:17:53Z","abstract_excerpt":"We study the Poincare polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the well-known investigation into the distribution of the Euler characteristic and Hodge numbers. We find interesting fractal behaviour in the roots of these polynomials in relation to the existence of isometries, distribution versus typicality, and mirror symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1612","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSYK+Y9STjHcN8XouSyyxBso683rcvfgUF5w0C4+Tif0J1LzVwnXW2dz7Z6lYmoB2XrrS0Ugv6HwhsN28nM8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:44:44.263295Z"},"content_sha256":"e7ce40372238872de4d8fcac5324b7331bd2eae6652816a61df6bf71df4d1a9e","schema_version":"1.0","event_id":"sha256:e7ce40372238872de4d8fcac5324b7331bd2eae6652816a61df6bf71df4d1a9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/bundle.json","state_url":"https://pith.science/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/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":"2026-05-26T14:44:44Z","links":{"resolver":"https://pith.science/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34","bundle":"https://pith.science/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/bundle.json","state":"https://pith.science/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHDD4AEZLTQJNGBJ6BH5SCZK34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MHDD4AEZLTQJNGBJ6BH5SCZK34","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":"650226998183638714762e0fe9aeeee7caeff5ba4ce53eb101c51f81f8958d85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-07T19:17:53Z","title_canon_sha256":"9bb422c1e64e9f9b7031b65cc987b0d43f4ff5063767725f3fecc44b844535f0"},"schema_version":"1.0","source":{"id":"1110.1612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1612","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1612v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1612","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"MHDD4AEZLTQJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MHDD4AEZLTQJNGBJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MHDD4AEZ","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:e7ce40372238872de4d8fcac5324b7331bd2eae6652816a61df6bf71df4d1a9e","target":"graph","created_at":"2026-05-18T00:50:13Z","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 study the Poincare polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the well-known investigation into the distribution of the Euler characteristic and Hodge numbers. We find interesting fractal behaviour in the roots of these polynomials in relation to the existence of isometries, distribution versus typicality, and mirror symmetry.","authors_text":"Anthony Ashmore, Yang-Hui He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-07T19:17:53Z","title":"Calabi-Yau Three-folds: Poincare Polynomials and Fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1612","kind":"arxiv","version":1},"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:e0e1880b7e562e677127ec9844f21846f0e253588cd28e1b66a81fca5de15e18","target":"record","created_at":"2026-05-18T00:50:13Z","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":"650226998183638714762e0fe9aeeee7caeff5ba4ce53eb101c51f81f8958d85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-07T19:17:53Z","title_canon_sha256":"9bb422c1e64e9f9b7031b65cc987b0d43f4ff5063767725f3fecc44b844535f0"},"schema_version":"1.0","source":{"id":"1110.1612","kind":"arxiv","version":1}},"canonical_sha256":"61c63e00995ce0969829f04fd90b2adf3654a93d5e83cbda4480b64b9a7fc8e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61c63e00995ce0969829f04fd90b2adf3654a93d5e83cbda4480b64b9a7fc8e7","first_computed_at":"2026-05-18T00:50:13.912737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.912737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+ziYM9CXK7ePHf94GqE3qeAZyGg42BVMgLdMwuVgHxv2LaeTGxzLUtXD8c7rk+atpaWSFQRFKqvwwIm9HkQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.913199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0e1880b7e562e677127ec9844f21846f0e253588cd28e1b66a81fca5de15e18","sha256:e7ce40372238872de4d8fcac5324b7331bd2eae6652816a61df6bf71df4d1a9e"],"state_sha256":"4a3426df22a46b16fa808b0d58d149fd25ca949a4615302a867c01931652382b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//S/G49+LqjfnHmwhtfEXHOQ4URTErnhgFWgiRTY/VB5kQIxWgW0LBpvGzuH8/OLq9iswfa/r6HjqwADCtMvCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:44:44.266753Z","bundle_sha256":"35985bca7121a00d0716c59874db95769070918591d207f71e8c07545c16e48a"}}