{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IANN7Z7UYEBN7POT25YK4SBIHF","short_pith_number":"pith:IANN7Z7U","canonical_record":{"source":{"id":"1507.01473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:14:31Z","cross_cats_sorted":[],"title_canon_sha256":"ef456d3b5cafb28f1382a00f169b4b796530a2b3377b0c0f3dd4c211b3f9444d","abstract_canon_sha256":"f6e225c58c91915215f86c36dbd7824dc6729327df02944cd6f868a8853a9e72"},"schema_version":"1.0"},"canonical_sha256":"401adfe7f4c102dfbdd3d770ae48283951f46a7f303175b62be50298f52bbfc5","source":{"kind":"arxiv","id":"1507.01473","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01473","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01473v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01473","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"IANN7Z7UYEBN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IANN7Z7UYEBN7POT","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IANN7Z7U","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IANN7Z7UYEBN7POT25YK4SBIHF","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:14:31Z","cross_cats_sorted":[],"title_canon_sha256":"ef456d3b5cafb28f1382a00f169b4b796530a2b3377b0c0f3dd4c211b3f9444d","abstract_canon_sha256":"f6e225c58c91915215f86c36dbd7824dc6729327df02944cd6f868a8853a9e72"},"schema_version":"1.0"},"canonical_sha256":"401adfe7f4c102dfbdd3d770ae48283951f46a7f303175b62be50298f52bbfc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.844867Z","signature_b64":"iktoceOkk9toVgezWAGEXPKZ4NUOTkIdB3fpJ2ythAkPsKFpX+KgbPDewZHA+tg8udOK8YuhHa67p3A/h8ZUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"401adfe7f4c102dfbdd3d770ae48283951f46a7f303175b62be50298f52bbfc5","last_reissued_at":"2026-05-18T01:37:16.844115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.844115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01473","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":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9Z37P32kOd/Pl75iT1AVXmoZXahxFA6sEIZ1S/Vg1IXD5ArssQ8fvUrFfseTflyL/JOFdMwWeSOfwO0HngkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:40:30.385579Z"},"content_sha256":"82012eb2c731934238a4d9be115a1f5af55900ac5631fdcb86e67bf1fc789b2a","schema_version":"1.0","event_id":"sha256:82012eb2c731934238a4d9be115a1f5af55900ac5631fdcb86e67bf1fc789b2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IANN7Z7UYEBN7POT25YK4SBIHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The recent status of the volume product problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. Makai Jr","submitted_at":"2015-07-06T14:14:31Z","abstract_excerpt":"In this small survey we consider the volume product, and sketch some of the best upper and lower estimates known up to now, based on our paper [BMMR]. The author thanks the organizers of the conference in Jurata, March 2010, for their kind invitation, and the excellent atmosphere there. This paper is based on the talk of the author on that conference."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01473","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":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYbJIJ5MFCgGhLIPm2xN4LyHHYMfSoTCyWR6zej9sNn5ToydeIRe0vS9T+wIcA3y3lpwiBS4C1nXWNbTgZmtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:40:30.385922Z"},"content_sha256":"5f2cd4a2e45a4d6f4c0d5303abf07801c0cdcdc1fee61b4965cc77a5a34adc9f","schema_version":"1.0","event_id":"sha256:5f2cd4a2e45a4d6f4c0d5303abf07801c0cdcdc1fee61b4965cc77a5a34adc9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IANN7Z7UYEBN7POT25YK4SBIHF/bundle.json","state_url":"https://pith.science/pith/IANN7Z7UYEBN7POT25YK4SBIHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IANN7Z7UYEBN7POT25YK4SBIHF/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":"2026-06-23T23:40:30Z","links":{"resolver":"https://pith.science/pith/IANN7Z7UYEBN7POT25YK4SBIHF","bundle":"https://pith.science/pith/IANN7Z7UYEBN7POT25YK4SBIHF/bundle.json","state":"https://pith.science/pith/IANN7Z7UYEBN7POT25YK4SBIHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IANN7Z7UYEBN7POT25YK4SBIHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IANN7Z7UYEBN7POT25YK4SBIHF","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":"f6e225c58c91915215f86c36dbd7824dc6729327df02944cd6f868a8853a9e72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:14:31Z","title_canon_sha256":"ef456d3b5cafb28f1382a00f169b4b796530a2b3377b0c0f3dd4c211b3f9444d"},"schema_version":"1.0","source":{"id":"1507.01473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01473","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01473v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01473","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"IANN7Z7UYEBN","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IANN7Z7UYEBN7POT","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IANN7Z7U","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5f2cd4a2e45a4d6f4c0d5303abf07801c0cdcdc1fee61b4965cc77a5a34adc9f","target":"graph","created_at":"2026-05-18T01:37:16Z","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 small survey we consider the volume product, and sketch some of the best upper and lower estimates known up to now, based on our paper [BMMR]. The author thanks the organizers of the conference in Jurata, March 2010, for their kind invitation, and the excellent atmosphere there. This paper is based on the talk of the author on that conference.","authors_text":"E. Makai Jr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:14:31Z","title":"The recent status of the volume product problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01473","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":"sha256:82012eb2c731934238a4d9be115a1f5af55900ac5631fdcb86e67bf1fc789b2a","target":"record","created_at":"2026-05-18T01:37:16Z","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":"f6e225c58c91915215f86c36dbd7824dc6729327df02944cd6f868a8853a9e72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-07-06T14:14:31Z","title_canon_sha256":"ef456d3b5cafb28f1382a00f169b4b796530a2b3377b0c0f3dd4c211b3f9444d"},"schema_version":"1.0","source":{"id":"1507.01473","kind":"arxiv","version":1}},"canonical_sha256":"401adfe7f4c102dfbdd3d770ae48283951f46a7f303175b62be50298f52bbfc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"401adfe7f4c102dfbdd3d770ae48283951f46a7f303175b62be50298f52bbfc5","first_computed_at":"2026-05-18T01:37:16.844115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.844115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iktoceOkk9toVgezWAGEXPKZ4NUOTkIdB3fpJ2ythAkPsKFpX+KgbPDewZHA+tg8udOK8YuhHa67p3A/h8ZUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.844867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82012eb2c731934238a4d9be115a1f5af55900ac5631fdcb86e67bf1fc789b2a","sha256:5f2cd4a2e45a4d6f4c0d5303abf07801c0cdcdc1fee61b4965cc77a5a34adc9f"],"state_sha256":"38d933efad578fce1313c3e430737a135fa16f53e624e2b7e5d70e889ac2f7e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1zkNAiLqQggPbFwqPuCVRY2wxu4FnsAwpVg4l5i6hu9ARg/LUloRUf+XxUTC+II7LlA/ujsY1B3R0m1YtZbeDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:40:30.387820Z","bundle_sha256":"baab1deee355d602f3e061b173af7a52f69f61761fe1e48d2effd910131ac1fc"}}